UNIT: TRANSFORMATIONS
Triangle XYZ is reflected across the x-axis, and X = (-11, 8). What are the coordinates of X' ? (11,-8) (-8, 11) (11, 8) (-11, -8)
(-11, -8)
Triangle XYZ is reflected across the y-axis, and X = (4, -5). What are the coordinates of X' ? (-5, 4) (-4, -5) (4, 5) (-4, 5)
(-4, -5)
If the triangle on the grid below is translated by using the rule , what will be the coordinates of ? (-4, 0) (0, 4) (0, 0) (-2, 2)
(-4, 0)
Which choice shows the coordinates of C' if the trapezoid is reflected across the y-axis? (-5, 3) (3, -5) (5, -3) (-3, 5)
(-5, 3)
What are the coordinates of A' after reflecting across the line x = 3? (2, 3) (3, 2) (3, 4) (3, -2)
(3, 2)
The point (4, 5) is translated two units left and eight units down. What is the y-coordinate of the image?
-3
A rotation maps point A to A'. Which statement describes the rotation? 270° counterclockwise rotation 90° clockwise rotation 180° rotation 90° counterclockwise rotation
180° rotation
Marissa wants to write an abbreviated set of directions for finding coordinates of a figure reflected across the y-axis. Which mapping notation is correct?
A
Tanya's rotation maps point K(24, -15) to K'(-15, -24). Which describes the rotation? clockwise rotation clockwise rotation rotation counterclockwise rotation
A
In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, , and . If , which statement is true? AB = 12.3 cm AB = 10.6 cm
AB = 10.6 cm
Which statement is true? A scalene triangle and a right triangle are always congruent. A scalene triangle and a right triangle are never congruent. An equilateral triangle and a right triangle are always congruent. An equilateral triangle and a right triangle are never congruent.
An equilateral triangle and a right triangle are never congruent.
Clayton needs to reflect the triangle below across the line . Which statements about the reflection are true? Check all that apply. Clayton could use the relationship to find the points of the image. Clayton could negate both the x and y values in the points to find the points of the image. C' will remain in the same location as C because it is on the line of reflection. C' will move because all points move in a reflection. The image and the pre-image will be congruent triangles. The image and pre-image will not have the same orientation because reflections flip figures.
Clayton could use the relationship to find the points of the image. C' will remain in the same location as C because it is on the line of reflection. The image and the pre-image will be congruent triangles. The image and pre-image will not have the same orientation because reflections flip figures.
After Hillary realized her clock was running 30 minutes fast, she used a knob on the clock to turn the minute hand back 30 minutes. Which describes the rotation of the minute hand? clockwise rotation clockwise rotation counterclockwise rotation counterclockwise rotation
D counterclockwise rotation
On a coordinate plane, point B(-6, 1) is translated to (-3, -2). Indira uses these steps to find a rule to describe the translation.Step 1Substitute the original coordinates and the translated coordinates into :Step 2Write two equations:Step 3Solve each equation:Step 4Write the translation rule:Which corrects Indira's first error? Indira should have substituted in Step 1. Indira should have written the equations and in Step 2. Indira should have solved the equations to find that and in Step 3. Indira should have written the translation rule in Step 4.
Indira should have written the equations and in Step 2.
Jorge needs to reflect a figure across the line . Which statements are correct regarding steps he could take to complete the reflection? Check all that apply. Jorge should graph in the vertical line with values of -4 for the line of reflection. Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection. Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side. Jorge will not move any point that lies on the line of reflection. Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection. Jorge could check his work by making sure that the image has the same orientation as the original.
Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection. Jorge will not move any point that lies on the line of reflection. Jorge could check his work by making sure that the image has the same orientation as the original.
The figure shows five points. A point has been translated right and up.Based on the graph, which statements about the points could be true? Check all that apply. Point D could be the image of B. Point C could be the image of A. Point E could be the image of C. Point D could be the image of A. Point E could be the image of B. Point C could be the image of E.
NOT Point D could be the image of B. Point C could be the image of A. Point E could be the image of C. Point C could be the image of E.
Arionna needed to graph triangle PQR reflected across the y-axis. Her work is shown below. Arionna's Work:Arionna's GraphWhich statements identify her errors? Check all that apply. Arionna did not find the correct point for P'. She should have negated the x-value, not the y-value. Arionna did not find the correct value for Q'. All points in a reflection will move. Arionna did not find the correct value for R'. She should have negated the y-value, not the x-value. Arionna's red triangle should be reflected below the horizontal axis rather than across the vertical axis. Arionna switched the order of the coordinates of P' (3, -7) when she graphed them.
NOT Arionna did not find the correct point for P'. She should have negated the x-value, not the y-value. Arionna did not find the correct value for Q'. All points in a reflection will move. Arionna switched the order of the coordinates of P' (3, -7) when she graphed them.
Which choice shows the coordinates of B' if the trapezoid is reflected across the x-axis? (-7, 2) (2, -7) (7, -2) (-2, 7)
NOT (-2, 7)
Triangle XYZ is reflected across the x-axis, and X = (-11, 8). What are the coordinates of X' ? (11,-8) (-8, 11) (11, 8) (-11, -8)
NOT (11,-8)
What are the coordinates of A' after reflecting across the line x = 3? (2, 3) (3, 2) (3, 4) (3, -2)
NOT (2, 3)
Triangle XYZ is reflected across the y-axis, and X = (4, -5). What are the coordinates of X' ? (-5, 4) (-4, -5) (4, 5) (-4, 5)
NOT (4, 5)
The shape below is transformed to another shape.Which shape could be its image?
NOT A
Arionna needed to graph triangle PQR reflected across the y-axis. Her work is shown below. Arionna's Work:Arionna's GraphWhich statements identify her errors? Check all that apply. Arionna did not find the correct point for P'. She should have negated the x-value, not the y-value. Arionna did not find the correct value for Q'. All points in a reflection will move. Arionna did not find the correct value for R'. She should have negated the y-value, not the x-value. Arionna's red triangle should be reflected below the horizontal axis rather than across the vertical axis. Arionna switched the order of the coordinates of P' (3, -7) when she graphed them.
NOT Arionna did not find the correct point for P'. She should have negated the x-value, not the y-value.
Parallelogram DEFG is transformed to parallelogram VSTU.Which statement about the transformation is true? Parallelogram DEFG is the pre-image because it is not the result of the transformation. Parallelogram DEFG is the image because it is the result of the transformation. Parallelogram VSTU is the pre-image because it is the result of the transformation. Parallelogram VSTU is the image because it is not the result of the transformation.
NOT B
Which graph shows the image of the triangle reflected across the line of reflection shown?
NOT C
The shape on the left is translated to the shape on the right.Which statement about the transformation is true? The name of the shape on the right is because it is the image of the shape on the left. The name of the shape on the right is because it is the pre-image of the shape on the left. The name of the shape on the right is because it is the pre-image of the shape on the left. The name of the shape on the right is because it is the image of the shape on the left.
NOT C The name of the shape on the right is because it is the pre-image of the shape on the left.
Which shows only a vertical translation from the shaded figure onto the unshaded figure?
NOT D
Which segment is the image of reflected across the line ?
NOT DC
On a coordinate plane, point B(-6, 1) is translated to (-3, -2). Indira uses these steps to find a rule to describe the translation.Step 1Substitute the original coordinates and the translated coordinates into :Step 2Write two equations:Step 3Solve each equation:Step 4Write the translation rule:Which corrects Indira's first error? Indira should have substituted in Step 1. Indira should have written the equations and in Step 2. Indira should have solved the equations to find that and in Step 3. Indira should have written the translation rule in Step 4.
NOT Indira should have substituted in Step 1.
Joaquin drew the triangle below.Which statement must be true about a figure that is congruent to Joaquin's triangle? It has two angles on the x-axis. It has a side that is 9 units long. It has a side that lies on the x-axis. It has an obtuse angle.
NOT It has two angles on the x-axis.
Which pair of segments in the figures below are congruent? and and and and
NOT c
If , what statement best describes triangle MON? The triangle is scalene. The triangle is equilateral. The triangle is isosceles and possibly equilateral. The triangle is isosceles but definitely not equilateral.
NOT d
Ryan wants to describe the translation shown on the grid below.Ryan uses the following steps to describe the translation.Step 1Identify the pre-image and the image:The pre-image is triangle XYZ, and the image is .Step 2Identify the number of units that each point moves horizontally:Each point moves one unit left.Step 3Identify the number of units that each point moves vertically:Each point moves three units down.Step 4The translation is one unit left and three units down.In which step did Ryan make the first error? Step 1 Step 2 Step 3 Step 4
NOT step 1
Which triangle is a translation of triangle P? triangle A triangle b triangle C triangle D
NOT triangle b
What is the equation for the line of reflection? x = 6 y = 6 y = x y = 2
NOT y = 6
Triangle RST is rotated 90° in a clockwise direction. What is the name of the image after the rotation? RST SRT
NOt SRT
Deepak is measuring sides and angles of triangle FGH to determine whether it is congruent to triangle MNP shown below.Deepak found that has a measure of 50° and is 18.3 centimeters long. Does he need to continue measuring sides and angles of triangle FGH and why? No, he knows that the triangles are congruent because there are corresponding sides and angles that are congruent. No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP. Yes, he must verify that the other two side lengths and the other two angle measures are the same as those found in triangle MNP. Yes, he must only verify that the other two angle measures are the same as those found in triangle MNP.
No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.
Parallelogram DEFG is transformed to parallelogram VSTU.Which statement about the transformation is true? Parallelogram DEFG is the pre-image because it is not the result of the transformation. Parallelogram DEFG is the image because it is the result of the transformation. Parallelogram VSTU is the pre-image because it is the result of the transformation. Parallelogram VSTU is the image because it is not the result of the transformation.
Parallelogram DEFG is the pre-image because it is not the result of the transformation.
Rectangle PQRS is rotated 90° counterclockwise about the origin.What are the coordinates of point Q'? Q'( -3, 5) Q'(3, -5) Q'(5, -3) Q'(-5, -3)
Q'( -3, 5)
Manuela claims that and are congruent.Which statement best describes her claim? She is incorrect because the segments do not have the same orientation. She is incorrect because the segments do not have the same length. She is correct because the segments have the same length. She is correct because the segments have the same orientation.
She is incorrect because the segments do not have the same length.
The graph below shows a transformation of the shaded rectangle onto the unshaded rectangle. Keesha says the transformation is a translation, but Teagan says that the transformation is a dilation. Which statement about the transformation is true? Keesha is correct because the shaded rectangle is moved vertically to make the unshaded rectangle. Keesha is correct because the shaded rectangle is flipped across a horizontal line. Teagan is correct because the unshaded rectangle is smaller than the shaded rectangle. Teagan is correct because the unshaded rectangle is turned in a clockwise direction.
Teagan is correct because the unshaded rectangle is smaller than the shaded rectangle.
Amber believes triangle ABC and triangle GFE are congruent. She has recorded the measures of some of the angles and the lengths of some of the sides in the triangles below. What additional measurement would support Amber's hypothesis? The measure of is 32°. The measure of is 40°. The measure of is 50°. The measure of is 90°.
The measure of is 40°.
A translation moves point V(-2, 3) to . Which are true statements about the translation? The point moves two units left and four units up. The transformation rule is . The transformation is a vertical translation. The image is four units to the left of the pre-image. The translation can be described as .
The transformation rule is . The transformation is a vertical translation.
Which statement correctly identifies the line of reflection? The triangles are reflected across the x-axis. The triangles are reflected across the y-axis. The triangles are reflected across the line y = x. The triangles are reflected across the line y = -x.
The triangles are reflected across the line y = x.
Linnea has drawn a line from one corner of a rectangle to the opposite corner. The line divides each of the right angles into two angles of measures 32° and 58°. Which statement best describes the resulting triangles? The two triangles are not congruent because the corresponding sides do not have the same length. The two triangles are congruent but are oriented differently. The two triangles may be congruent, but additional information is needed about the angle measures. The two triangles may be congruent, but additional information is needed about the side lengths.
The two triangles are congruent but are oriented differently.
The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.Which statement about the transformation is true? The unshaded octagon is a reflection because it is a flip over a diagonal line. The unshaded octagon is a dilation because it is smaller than the shaded octagon. The unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon. The unshaded octagon is a vertical translation because it is directly under the shaded octagon.
The unshaded octagon is a reflection because it is a flip over a diagonal line.
Iliana rotated trapezoid WXYZ 180° about the origin. What is the correct set of image points for trapezoid W'X'Y'Z'? W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2) W'(4, 2), X'(3, 4), Y'(1, 4), Z'(0, 2) W'(-2, -4), X'(-4, -3), Y'(-4, -1), Z'(-2, 0) W'(2, 4), X'(4, 3), Y'(4, 1), Z'(2, 0)
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
If WZYX PMLN describes two quadrilaterals, which other statement is also true? WXYZ LMNP WXYZ NPML WXYZ PNLM WXYZ MLNP
WXYZ PNLM
If hexagon JGHFKI hexagon SRTQUV, which pair of angles must be congruent? and and and and
a
Marissa wants to write an abbreviated set of directions for finding coordinates of a figure reflected across the y-axis. Which mapping notation is correct?
a
Pentagon JKLMN is translated five units up. What is the name of the image after the translation? JKLMN NMLKJ
a
The shape on the left is transformed to the shape on the right.Which of the following statements describes the transformation?
a
Which rule describes the translation below?
a
Which statement describes the congruent triangles?
a
If describes two triangles, which other statement is also true?
b
Rectangle GHIJ is dilated to be a smaller shape. What is the name of the image after the dilation? GHIJ IGJH
b
The shape on the left is transformed to the shape on the right.Which of the following statements describes the transformation?
b
The triangle on the grid will be translated two units left.Which shows the triangle when it is translated two units left?
b
Which graph shows a method for finding the image of point D if the parallelogram is reflected across the dashed line? Submitted
b
If WZYX PMLN describes two quadrilaterals, which other statement is also true? WXYZ LMNP WXYZ NPML WXYZ PNLM WXYZ MLNP
c
The triangle on the grid will be translated two units down.Which shows the triangle when it is translated two units down?
c
The triangle on the grid will be translated two units down.Which shows the triangle when it is translated two units down? Submitted
c
Which statement describes this pair of congruent triangles?
c
Heart 1 is translated 3 units down to heart 2. Which shows this transformation?
d
Lincoln is measuring the angles of quadrilateral WXYZ to determine whether it is congruent to the quadrilateral below.Which pair of measurements are possible if they are congruent figures? and and and and
d
The shape below is transformed to another shape.Which shape could be its image?
d
Which graph shows the image of the triangle reflected across the line of reflection shown?
d
Which pair of segments in the figures below are congruent? and and and and
d
The triangles on the grid below represent a translation.To form the image, the pre-image moved five units right and three units up. two units right and three units up. five units left and three units down. two units left and three units down.
five units right and three units up.
A triangle is translated by using the rule . Which describes how the figure is moved? four units left and one unit down four units left and one unit up one unit right and four units down one unit right and four units up
four units left and one unit up
Four students are trying to find the rule that translates point N(-2, -4) to . Each student's reasoning is shown below. Raheem:The rule is because and .Casey:The rule is because the image is (2, 4).Andrew:The rule is because the coordinates are opposites.Lo:The rule is because and .Which student is correct? Raheem Casey Andrew Lo
lo
What is the name of the transformation in which each point on a figure is turned through a given angle and direction around a given point?
rotation
Ryan wants to describe the translation shown on the grid below.Ryan uses the following steps to describe the translation.Step 1Identify the pre-image and the image:The pre-image is triangle XYZ, and the image is .Step 2Identify the number of units that each point moves horizontally:Each point moves one unit left.Step 3Identify the number of units that each point moves vertically:Each point moves three units down.Step 4The translation is one unit left and three units down.In which step did Ryan make the first error? Step 1 Step 2 Step 3 Step 4
step 3
Which image is a reflection of the black polygon in quadrant I? the black polygon in quadrant I the red polygon in quadrant II the blue polygon in quadrant III the green polygon in quadrant IV
the red polygon in quadrant II
Triangle PQR is reflected across a line, P = (4,-5), and P' = (-4, -5). What is the line of reflection? the x-axis the y-axis the line y = x the line y = -x
the y-axis
Rectangle JKLM is congruent to a 4 inch by 7 inch rectangle. How many different values are possible for the length of ? one two three four
two
Which rule can be used to describe the x-coordinates in the translation below?. x + 0 x + 6 x - 6 x + 2
x + 0
What is the equation for the line of reflection? x = 3 y = 3 y = x x = 6
x = 3
What is the line of reflection for the trapezoids? x = 3 y = 3 x-axis y-axis
x = 3