geometry exam

A line segment has endpoints at (-4, -6) and (-6, 4). Which reflection will produce an image with endpoints at (4, -6) and (6, 4)?

a reflection of the line segment across the y-axis

What are the coordinates of vertex F" of ΔF"G"H"?

(4, -1.5)

What is the relationship between RR' and SS'?

RR' || SS'

dilation

Which transformation maps the pre-image to the image?

Which transformation maps the pre-image, DEFG, to the image, D'E'F'G'?

The transformation is a reflection.

Which describes the transformation? Select three options.

it is rigid, it is isometric, the size is preserved

Which statements must be true about the reflection of ΔXYZ across ? Select three options.

m∠X'Z'Y' = 90° m∠MCY = 90° BZ' ≅ BZ

Which transformation maps the pre-image to the image?

reflection

What is the rule for the reflection?

ry=x(x, y) → (y, x)

Which transformation maps the pre-image to the image?

stretch

What is L'L?

5 units

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

(x, y) → (x - 3, y + 5)

A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule?

(x, y) → (x - 8, y + 4)

Which triangle shows the final image?

1

Which description is true about the transformation shown?

It is a dilation because the transformation is not isometric.

Quadrilateral ABCD is transformed according to the rule (x, y) → (y, -x). Which is another way to state the transformation?

R0, 270°

One vertex of a polygon is located at (3, -2). After a rotation, the vertex is located at (2, 3). Which transformations could have taken place? Select two options.

R0, 90° and R0, -270°

Rectangle ABCD has vertices A(-6, -2), B(-3, -2),C(-3. -6), and D(-6, -6). The rectangle is translated so that the coordinates of the image are A'(-10, 1), B'(-7,1),C'(-7, -3), and D'(-10, -3). Which rule was used to translate the image?

T-4, 3(x, y)

Which side in the image corresponds to in the pre-image?

TV

Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options.

The rule for the translation can be written as T3, -5(x, y). Triangle ABC has been translated 3 units to the right and 5 units down.

If a translation of T2, -7(x, y) is applied to ΔABC, what are the coordinates of B'?

(3, -12)

Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?

(3, 2)

Which point would map onto itself after a reflection across the line y = -x?

(4, -4)

What are the coordinates of the image of vertex D after a reflection across the x-axis?

(5, 3)

What is YT?

12 units

What is y, the distance between points R and R'?

3 units

Irina wants to tile her floor using the translation shown below. Which is the rule for this translation?

T-3, 2(x, y)

A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The triangle is transformed according to the rule R0, 180°. Which statements are true regarding the transformation? Select three options.

The rule for the transformation is (x, y) → (-x, -y). The coordinates of L' are (-2,-2). The coordinates of N' are (-1,-6).

Which composition of transformations maps figure EFGH to figure E"F"G"H"?

a reflection across line k followed by a translation down

The first transformation for this composition is [________], and the second transformation is a 90° rotation about point X'.

a reflection across line m

What is the final transformation in the composition of transformations that maps pre-image GHJK to image G'H"J"K"?

a reflection across line m

A point has the coordinates (0, k). Which reflection of the point will produce an image at the same coordinates, (0, k)?

a reflection of the point across the y-axis

The rule as a mapping for the translation of a rectangle is (x, y) → (x - 2, y + 7). Which describes this translation?

a translation of 2 units to the left and 7 units up

What are the coordinates of vertex F of parallelogram FGHJ?

(-4, 2)

What are the coordinates of the pre-image of B'?

(-8, -2)

RR'= 12. What is the length of RZ?

6

Triangle ABC was transformed using the rule (x, y) → (-y, x). The vertices of the triangles are shown. A (-1, 1)B (1, 1)C (1, 4) A' (-1, -1)B' (-1, 1)C' (-4, 1) Which best describes the transformation?

The transformation was a 90° rotation about the origin.

What are the coordinates of the image of vertex G after a reflection across the line y = x?

(-5, 4)

Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are(-9, 2), what are the coordinates of F'?

(-6, -6)

Which rule represents the translation from the pre-image, ABCD, to the image, A'B'C'D'?

T2, 1(x, y)

What are the coordinates of point W" on the final image?

(3, 8)

What are the coordinates of point K" on the final image?

(4, -7)

Triangle ABC is translated according to the rule (x, y) → (x + 2, y - 8). If the coordinates of the pre-image of point B are(4, -5), what are the coordinates of B'?

(6, -13)

Which rule describes the transformation?

(x, y) → (y, -x)

What is OB'?

3 units

Which statement best describes one of these transformations?

Triangle 1 is rotated to result in triangle 2.

Is this a rigid transformation? Explain. = 10 cm = 10 cm = 9 cm = 9 cm = 4 cm = 4 cm

Yes, the pre-image and image have the same side length measures.

Which statement about the transformation is true?

It is not isometric because the side lengths did not remain the same.

One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0). Which transformations could have taken place? Select two options.

R0, 270° and R0, -90°

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(-1, 2). The image of triangle XYZ after a rotation has verticesX'(-3, 1), Y'(0, 0), and Z'(-2, -1). Which rule describes the transformation?

R0, 90°