Geometry B v.2 : 4. TRANSFORMATIONS

An isometry does not preserve _____. one-to-one correspondence distance shape orientation

orientation

Which of the following are rigid motion transformations? dilation similarity reflection translation rotation

reflection translation rotation

The coordinates of a triangle are given as A(3, 2), B(-4, 1) and C(-3, -2). What are the coordinates of the image after the triangle is reflected in the line y=x? A'( a0, a1) B'(a2, a3) C'(a4, a5)

a0 = 2 a1 = 3 a2 = 1 a3 = -4 a4 = -2 a5 = -3

Which of the following is a validation of congruency between two polygons? if by applying dilation you can make them equal if by applying only rotation you can make them coincide if by applying rigid motions you can make them coincide if by applying only translation you can make them coincide

if by applying rigid motions you can make them coincide

Which of the following is a name for an isometry that moves or maps every point of the plane the same distance and direction? Select all that apply. slide rotation glide translation flip

slide glide translation

The key idea of the transformation called translation is _____. the gliding or sliding of every point in the plane the same direction the object moves the plane a certain angle measure the rotating of a plane about a fixed point the object and its image have opposite orientations

the gliding or sliding of every point in the plane the same direction

A transformation T: (x, y) --> (x - 5, y + 3). The image of A(2, -1) is (3, 2) (-3, -2) (-3, 2)

(-3, 2)

A transformation T: (x, y) (x + 3, y + 1). For the ordered pair (4, 3), enter its preimage point. (-1, 2) (7, 4) (1, 2)

(1, 2)

If a translation maps point (3, 2) to (4, 5); or T: (3, 2) (4, 5), then what is the image of the point (0, 0)? (1, 3) (-1, -3) (4, 5)

(1, 3)

In a reflection across the x-axis a given coordinate (2, -1) transforms itself into which of the following? (-2, 0) (2, 1) (0, 1) (-2, 1)

(2, 1)

A transformation T : (x, y) --> (x + 3, y + 1). The image of B(4, 1) is (1, 0) (-1, 0) (7, 2)

(7, 2)

Match the following items. In the figure below, several reflections are illustrated. Note one line of symmetry is m and one is l. Pay close attention to the line of reflection being indicated by R l and R m. https://dw6y82u65ww8h.cloudfront.net/organisations/328/f5591225-d674-41f1-9366-c35b0b617288/qu09010.gif 1.R l : Z 2.R l : T 3.R l : B 4.R m : S 5.R l : F 6.R l : S S Q Y B F X

1. X 2. Q 3. F 4. Y 5. B 6. S

Using this figure, the image of A is ______. https://dw6y82u65ww8h.cloudfront.net/organisations/328/16f7c034-653f-413b-9f78-0b80122db0ab/model1.gif A' B' A" B"

A'

The parallelogram is reflected across the line y = x. Which of the following are coordinates of a vertex of the image? https://dw6y82u65ww8h.cloudfront.net/organisations/328/f5591225-d674-41f1-9366-c35b0b617288/img_geo_10_2_rev1_1_3_reflection_assess1.gif D'(1, 3) B'(-3, -4) A'(1, -5) C'(-1, -2)

A'(1, -5)

A transformation named T maps triangle XYZ to triangle X'Y'Z'. The transformation is a(n) _____. https://dw6y82u65ww8h.cloudfront.net/organisations/328/28178588-96c3-4c08-afda-e9ba9df38d7d/l10093q.gif Rotation Reflection Dilation Isometry

Isometry

Select all that apply. A polygon is reflected across a line. The angles in the original figure are compared to the corresponding angles in the image to see if they are congruent. Which factors does this depend upon? None of these. They will always be congruent. The angle measures of the polygon. The line of reflection. The number of sides of the polygon

None of these. They will always be congruent.

A triangle is reflected across the line x = 2. Which of the following is true? The image and pre-image have the same orientation. The image and pre-image have different sizes. The image and the pre-image are congruent. The image and pre-image are separated by a given angle.

The image and the pre-image are congruent.

A transformation named T maps triangle XYZ onto triangle X'Y'Z'. The image of Y is ____. https://dw6y82u65ww8h.cloudfront.net/organisations/328/28178588-96c3-4c08-afda-e9ba9df38d7d/l10093q.gif X Y" Y' X'

Y'

What are the coordinates of the image of triangle ABC after it is translated according to (x,y)→(x+2,y−4)? https://dw6y82u65ww8h.cloudfront.net/organisations/328/28178588-96c3-4c08-afda-e9ba9df38d7d/img_geo_10_3_rev1_2_4_translation_assess2.gif A'(a0, a1) B'(a2, a3) C'(a4, a5)

a0 = -1 a1 = -2 a2 = 3 a3 = 1 a4 = 4 a5 = -7

Choose the option that best completes the statement. Following a translation, the measures of the angles in a pre-image _____. are at the same angle displacement about a given point. are larger or smaller based on the scale factor used of the corresponding angles in its image. are in the opposite orientation of the corresponding angles in its image. are congruent to the measures of the corresponding angles in its image.

are congruent to the measures of the corresponding angles in its image.

Which of the following is not an isometry? translation dilation rotation

dilation

An isometry is a transformation that preserves distance direction orientation

distance

An isometry is a transformation that preserves distance orientation direction

distance

Using this figure, the transformation shown is a ________. https://dw6y82u65ww8h.cloudfront.net/organisations/328/16f7c034-653f-413b-9f78-0b80122db0ab/model1.gif reflection rotation translation

translation

What translation was used on ABCD to produce A'B'C'D'? https://dw6y82u65ww8h.cloudfront.net/organisations/328/28178588-96c3-4c08-afda-e9ba9df38d7d/img_geo_10_3_rev1_2_3_translaton_assess1.gif ( x, y)→( x - 4, y + 3) ( x, y)→( x - 3, y + 4) ( x, y)→( x + 4, y + 3) ( x, y)→( x + 4, y - 3)

( x, y)→( x - 4, y + 3)

Which of the following statements is true of a reflection? Select all that apply. It changes the size of the figure being reflected. It is an isometry. It flips a plane about a fixed line. The transformation is done over a line of reflection. It slides a plane.

It is an isometry. It flips a plane about a fixed line. The transformation is done over a line of reflection.

The key idea of the transformation called a reflection is _____. the rotating of a plane about a fixed point the object moves in a straight line movement the object moves the plane a certain angle measure the object and its image have opposite orientations

the object and its image have opposite orientations