AnswersGeometry with StatisticsGeometric Transformations

Geometric Transformations — Test Answers

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Which statements are true about the reflectional symmetry of a regular heptagon? Choose two correct answers.

A
It has 7-fold symmetry.
B
A line of symmetry will connect the midpoints of 2 opposite sides.
C
A line of symmetry will connect 2 vertices.
D
A line of symmetry will connect a vertex and a midpoint of an opposite side.
E
It has only 1 line of reflectional symmetry.
2
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Triangle ABC is shown on the graph. What are the coordinates of the image of point cap b after the triangle is rotated 270 degrees about the origin?

A
open paren negative 4 comma negative 2 close paren
B
open paren negative 2 comma negative 4 close paren
C
open paren 4 comma 2 close paren
D
open paren 2 comma 4 close paren
3

The first transformation for this composition is [________], and the second transformation is a reflection across line c

A
a 180 degrees rotation about point cap h
B
a translation down and to the left
C
a 180 degrees rotation about point cap g
D
a translation up and to the right
4

What are the coordinates of the image of vertex cap f after a reflection across the line y is equal to negative x ?

A
open paren 1 comma 3 close paren
B
open paren negative 1 comma negative 3 close paren
C
open paren 3 comma negative 1 close paren
D
open paren negative 3 comma 1 close paren
5

Which statements are true about the relationship between the figures? Choose three correct answers.

A
Angle C prime will have the same measure as angle A .
B
Angle D prime will have the same measure as angle B .
C
Quadrilateral A prime B prime C prime D prime is an isometric transformation of quadrilateral A B C D .
D
Segment C prime D prime cannot be obtained through an isometric transformation of segment A D .
E
Segment A B can be obtained through an isometric transformation of segment B C .
6

If the trapezoid is the image of a translation of F G H J , what must be true of F G H J ?

A
J H must be perpendicular to H prime J prime .
B
F J must be parallel to G H .
C
F G must have the same measure as h j .
D
J J prime must be the same distance as H H prime .
7

Which statement about the transformation is true?

A
It is nonrigid because no side lengths or angles are congruent.
B
It is rigid because no side lengths or angles are congruent.
C
It is rigid because all side lengths and angles are congruent.
D
It is nonrigid because all side lengths are congruent.
8

Which rule describes the transformation?

A
open paren x comma y close paren rightarrow open paren x comma negative y close paren
B
open paren x comma y close paren rightarrow open paren y comma x close paren
C
open paren x comma y close paren rightarrow open paren negative y comma negative x close paren
D
open paren x comma y close paren rightarrow open paren negative x comma negative y close paren
9

How many lines of symmetry does the shape have?

A
4
B
2
C
0
D
1
10

The function rule cap t sub negative 4 comma 6 times open paren x comma y close paren could be used to describe which translation?

A
a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
B
a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right
C
a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left
D
a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up
11

How many lines of reflectional symmetry does the trapezoid have?

A
2
B
0
C
3
D
1
12

Which transformation maps the large triangle onto the small triangle?

A
translation
B
dilation
C
reflection
D
rotation
13

Emma reflected the triangle across the x -axis and then rotated the figure 90 degrees counterclockwise about the origin. Which triangle cap A prime cap b prime cap c prime did she end up with?

A
Image with description On a coordinate plane, a triangle has point A prime at 1 comma 1, point B prime at 3 comma 2, and point C prime at 4 comma 1.
B
Image with description On a coordinate plane, a triangle has point A prime at negative 2 comma 4, point B prime at negative 1 comma 2, and point C prime at negative 2 comma 1.
C
Image with description On a coordinate plane, a triangle has point A prime at negative 1 comma 1, point B prime at negative 3 comma 2, and point C prime at negative 4 comma 1.
D
Image with description On a coordinate plane, a triangle has point A prime at 1 comma 1, point B prime at 2 comma 3, and point C prime at 1 comma 4.
14

What is m angle YXS ?

A
180 degrees
B
45 degrees
C
90 degrees
D
270 degrees
15

Square RSTU is translated to form cap r prime cap s prime cap t prime cap u prime , which has vertices cap r prime times open paren negative 8 comma 1 close paren , cap s prime times open paren negative 4 comma 1 close paren , cap t prime times open paren negative 4 comma negative 3 close paren , and cap u prime times open paren negative 8 comma negative 3 close paren If point cap s has coordinates of open paren 3 comma negative 5 close paren , which point lies on a side of the pre-image, square RSTU ?

A
open paren negative 1 comma negative 6 close paren
B
open paren negative 5 comma negative 3 close paren
C
open paren 3 comma negative 3 close paren
D
open paren 4 comma negative 9 close paren
16

What are two possible transformations that together could have been used to create figure cap A prime cap b prime cap c prime cap d prime from figure ABCD ?

A
a rotation of 90 degrees counterclockwise about the origin followed by a translation of 2 units up
B
a translation of 2 units up followed by a reflection across the x - axis
C
a translation of 2 units up followed by a translation of 4 units right
D
a reflection across the y axis followed by a translation of 2 units up
17

Trapezoid A B C D is transformed according to the rule r sub x minus A x i s raised to the circ power R sub 0 comma 90 degrees What is the x -coordinate of A double prime ?

A
negative 2
B
negative 3
C
2
D
3
18

At which angle will the hexagon rotate so that it maps onto itself?

A
90 degrees
B
180 degrees
C
120 degrees
D
60 degrees
19

How many lines of symmetry does the shape have?

A
4
B
2
C
5
D
3
20

Quadrilateral L M N O is transformed according to the rule T negative 2 comma 4 What are the coordinates of L prime ?

A
9 comma 3
B
3 comma 5
C
3 comma negative 3
D
9 comma negative 1

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