Question 1

Solve the problem.
-A rotation has sent A to A' and E to E'. Find the image of the given figure.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

Solve the problem.
-Find the image of the given figure under a reflection across the mirror line m.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Solve the problem.
-A glide reflection is defined by the given slide arrow and the line of reflection m. Find the image of the given figure under this glide reflection.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Solve the problem.
-Find the equation of the line through $( 1,0 )$ and perpendicular to $x = 7$.

Accepted Answer

A)  $y = 7$ 
B)  $x = 0$ 
C)  $y = 0$ 
D)  $x = - 7$ 
A)  $y = 7$ 
B)  $x = 0$ 
C)  $y = 0$ 
D)  $x = - 7$

Question 5

Solve the problem.
-Find the image of the given figure under the translation that takes P to P'.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Find the coordinates of the image for the given point under the translation defined by $ (x, y) \rightarrow(x+4, y-2) $
-( -6, -7)

Accepted Answer

A) ( -10, -9) 
B) ( -10, -5) 
C) ( -2, -5) 
D) ( -2, -9) 
A) ( -10, -9) 
B) ( -10, -5) 
C) ( -2, -5) 
D) ( -2, -9)

Question 7

Find the coordinates of the image for the given point under the translation defined by $ (x, y) \rightarrow(x+4, y-2) $
-(6, 3)

Accepted Answer

A) (2, 5) 
B) (2, 1) 
C) (10, 5) 
D) (10, 1) 
A) (2, 5) 
B) (2, 1) 
C) (10, 5) 
D) (10, 1)

Question 8

Solve the problem.
-Find the image of the given figure under the translation that takes P to P'.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Solve the problem.
-Find the image of the given figure under a reflection across the mirror line m.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Solve the problem.
-The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Solve the problem.
-The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Find the coordinates of the image for the given point under the translation defined by $ (x, y) \rightarrow(x+4, y-2) $
-(0, 4)

Accepted Answer

A) (4, 6) 
B) ( -4, 2) 
C) ( -4, 6) 
D) (4, 2) 
A) (4, 6) 
B) ( -4, 2) 
C) ( -4, 6) 
D) (4, 2)

Question 13

Solve the problem.
-The image of a figure is given for a rotation that takes A to A' and D to D'. Find the original figure. Note again, the given figure is the image after rotation.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

For the given point, find the coordinates of the image point under a half-turn about the origin.
-(2, 0)

Accepted Answer

A) (0, -2) 
B) (0, 0) 
C) ( -2, 0) 
D) (0, 2) 
A) (0, -2) 
B) (0, 0) 
C) ( -2, 0) 
D) (0, 2)

Question 15

Solve the problem.
-Shown is the image of a figure under the two successive translations that take P to P' and then P' to P''. Find the original figure. Note again, the given figure is the image after translation. Hint: First
Find the final image of a point if it were translated by both translations. Then what happens in the
Reverse process?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Solve the problem.
-Find the image of the given figure under the reflection that sends P to P'.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Solve the problem.
-Points $\mathrm { A } ( - 1 , - 2 ) , \mathrm { B } ( 2 , - 3 )$, and $\mathrm { C } ( - 3 , - 8 )$ are given. Find all possible coordinates of point $\mathrm { D }$ such that the four points form a rectangle. For each location of point D found, find a translation that will take $\overline { \mathrm { AB } }$ to the opposite side of the rectangle formed.

Accepted Answer

A)  $\mathrm { D } ( 1 , - 11 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x + 1 , y + 3 )$. 
B)  $\mathrm { D } ( 3 , - 9 )$; $A$ translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 3 , y - 1 )$. 
C)  $\mathrm { D } ( 0 , - 9 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 2 , y - 6 )$. 
D)  $\mathrm { D } ( - 2 , - 8 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 6 , y - 2 )$. 
A)  $\mathrm { D } ( 1 , - 11 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x + 1 , y + 3 )$. 
B)  $\mathrm { D } ( 3 , - 9 )$; $A$ translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 3 , y - 1 )$. 
C)  $\mathrm { D } ( 0 , - 9 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 2 , y - 6 )$. 
D)  $\mathrm { D } ( - 2 , - 8 )$; A translation that takes $\overline { \mathrm { AB } }$ to $\overline { \mathrm { CD } }$ such that the image of $\mathrm { A }$ is $\mathrm { C }$ and the image of $\mathrm { B }$ is $D$ is $( x , y ) \rightarrow ( x - 6 , y - 2 )$.

Question 18

Solve the problem.
-The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Solve the problem.
-Find the image of the given figure under a reflection across the mirror line m.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Solve the problem.
-Find the equation of the image of the line $y = \bar { x } - 1$ when the reflection line is the $y$-axis.

Accepted Answer

A)  $y = - x + 1$ 
B)  $y = - x - 1$ 
C)  $y = x - 1$ 
D)  $y = x + 1$ 
A)  $y = - x + 1$ 
B)  $y = - x - 1$ 
C)  $y = x - 1$ 
D)  $y = x + 1$

Solve the problem. -A rotation has sent A to A' and E to E'. Find the image of the given figure.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -A glide reflection is defined by the given slide arrow and the line of reflection m. Find the image of the given figure under this glide reflection.

Solve the problem. -Find the equation of the line through $( 1,0 )$ and perpendicular to $x = 7$ .

Solve the problem. -Find the image of the given figure under the translation that takes P to P'.

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -( -6, -7)

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -(6, 3)

Solve the problem. -Find the image of the given figure under the translation that takes P to P'.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -(0, 4)

Solve the problem. -The image of a figure is given for a rotation that takes A to A' and D to D'. Find the original figure. Note again, the given figure is the image after rotation.

For the given point, find the coordinates of the image point under a half-turn about the origin. -(2, 0)

Solve the problem. -Find the image of the given figure under the reflection that sends P to P'.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -Find the equation of the image of the line $y = \bar { x } - 1$ when the reflection line is the $y$ -axis.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Area, Pythagorean Theorem, and Volume

Filters

Exam 13: Congruence and Similarity With Transformations

Solve the problem. -A rotation has sent A to A' and E to E'. Find the image of the given figure.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -A glide reflection is defined by the given slide arrow and the line of reflection m. Find the image of the given figure under this glide reflection.

Solve the problem. -Find the equation of the line through (1,0)( 1,0 )(1,0) and perpendicular to x=7x = 7x=7 .

Solve the problem. -Find the image of the given figure under the translation that takes P to P'.

Find the coordinates of the image for the given point under the translation defined by (x,y)→(x+4,y−2) (x, y) \rightarrow(x+4, y-2) (x,y)→(x+4,y−2) -( -6, -7)

Find the coordinates of the image for the given point under the translation defined by (x,y)→(x+4,y−2) (x, y) \rightarrow(x+4, y-2) (x,y)→(x+4,y−2) -(6, 3)

Solve the problem. -Find the image of the given figure under the translation that takes P to P'.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Find the coordinates of the image for the given point under the translation defined by (x,y)→(x+4,y−2) (x, y) \rightarrow(x+4, y-2) (x,y)→(x+4,y−2) -(0, 4)

Solve the problem. -The image of a figure is given for a rotation that takes A to A' and D to D'. Find the original figure. Note again, the given figure is the image after rotation.

For the given point, find the coordinates of the image point under a half-turn about the origin. -(2, 0)

Solve the problem. -Find the image of the given figure under the reflection that sends P to P'.

Solve the problem. -The image of a figure under the translation that takes P to P' is shown. Find the original figure. Note again, the given figure is the image after translation.

Solve the problem. -Find the image of the given figure under a reflection across the mirror line m.

Solve the problem. -Find the equation of the image of the line y=xˉ−1y = \bar { x } - 1y=xˉ−1 when the reflection line is the yyy -axis.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Area, Pythagorean Theorem, and Volume

Filters

Solve the problem. -Find the equation of the line through $( 1,0 )$ and perpendicular to $x = 7$ .

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -( -6, -7)

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -(6, 3)

Find the coordinates of the image for the given point under the translation defined by $(x, y) \rightarrow(x+4, y-2)$ -(0, 4)

Solve the problem. -Find the equation of the image of the line $y = \bar { x } - 1$ when the reflection line is the $y$ -axis.