Question 1

Find the coordinates of the image for the given point under the translation defined by $ (x, y) \rightarrow(x+4, y-2) $
-(0, 6)

Accepted Answer

A) (4, 8) 
B) (4, 4) 
C) ( -4, 4) 
D) ( -4, 8) 
A) (4, 8) 
B) (4, 4) 
C) ( -4, 4) 
D) ( -4, 8) B

Question 2

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) ( -8, 5) 
B) ( -8, 9) 
C) ( -2, 9) 
D) ( -2, 5) 
A) ( -8, 5) 
B) ( -8, 9) 
C) ( -2, 9) 
D) ( -2, 5) D

Question 3

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

Accepted Answer

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

Question 4

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 5

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 6

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

Accepted Answer

A) ( -1, 4) 
B) (7, 4) 
C) (7, 8) 
D) ( -1, 8) 
A) ( -1, 4) 
B) (7, 4) 
C) (7, 8) 
D) ( -1, 8)

Question 7

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

Accepted Answer

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

Question 8

Solve the problem.
-A figure ABCDEF and its image A'B'C'D'E'F' after a rotation are given. Which point of the grid is the center of rotation?

Accepted Answer

A)  $B$ 
B)  $S$ 
C)  $Q$ 
D)  $P$ 
A)  $B$ 
B)  $S$ 
C)  $Q$ 
D)  $P$

Question 9

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

Question 10

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 11

For the given point, find the coordinates of the image point under a half-turn about the origin.
-(2, -3)

Accepted Answer

A) (3, -2) 
B) ( -3, 2) 
C) ( -2, 3) 
D) (2, 3) 
A) (3, -2) 
B) ( -3, 2) 
C) ( -2, 3) 
D) (2, 3)

Question 12

Solve the problem.
-A figure and its image under a rotation are given. Which point of the grid is the center of rotation?

Accepted Answer

A)  $\mathrm { S }$ 
B)  $P$ 
C)  $Q$ 
D)  $\mathrm { R }$ 
A)  $\mathrm { S }$ 
B)  $P$ 
C)  $Q$ 
D)  $\mathrm { R }$

Question 13

Solve the problem.
-Find the image of the given figure under a 90° counterclockwise rotation about P.

Accepted Answer

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

Question 14

Solve the problem.
-Find the equation of the image of the line $y = x + 9$ when reflected in the $x$-axis.

Accepted Answer

A)  $y = - x - 9$ 
B)  $y = x - 9$ 
C)  $\mathrm { y } = - \mathrm { x } + 9$ 
D)  $y = x + 9$ 
A)  $y = - x - 9$ 
B)  $y = x - 9$ 
C)  $\mathrm { y } = - \mathrm { x } + 9$ 
D)  $y = x + 9$

Question 15

Solve the problem.
-Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = - 4 x + 4$.

Accepted Answer

A)  $y = \frac { 1 } { 4 } x + 8$ 
B)  $y = \frac { 1 } { 4 } x - 8$ 
C)  $y = - 4 x - 8$ 
D)  $y = - \frac { 1 } { 4 } x - 8$ 
A)  $y = \frac { 1 } { 4 } x + 8$ 
B)  $y = \frac { 1 } { 4 } x - 8$ 
C)  $y = - 4 x - 8$ 
D)  $y = - \frac { 1 } { 4 } x - 8$

Question 16

Solve the problem.
-Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = x + 2$.

Accepted Answer

A)  $y = -x - 8$ 
B)  $y = -x + 8$ 
C)  $y = x - 8$ 
D)  $y = x + 8$ 
A)  $y = -x - 8$ 
B)  $y = -x + 8$ 
C)  $y = x - 8$ 
D)  $y = x + 8$

Question 17

Solve the problem.
-Find the image of the given figure under a 180° rotation about P.

Accepted Answer

A)

B) 
  
C) 
  
D) 
  
A)

B) 
  
C) 
  
D)

Question 18

Solve the problem.
-Find the figure that results from reflecting the given figure across the line m, and then reflecting the result across line n.

Accepted Answer

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

Question 19

Solve the problem.
-If the given figure goes through a 90° clockwise rotation about P, followed by a 90° counterclockwise rotation of the resulting figure about Q, find the final image.

Accepted Answer

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

Question 20

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)

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

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

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 the reflection that sends P to P'.

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

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

Solve the problem. -A figure ABCDEF and its image A'B'C'D'E'F' after a rotation are given. Which point of the grid is the center of rotation?

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

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.

For the given point, find the coordinates of the image point under a half-turn about the origin. -(2, -3)

Solve the problem. -A figure and its image under a rotation are given. Which point of the grid is the center of rotation?

Solve the problem. -Find the image of the given figure under a 90° counterclockwise rotation about P.

Solve the problem. -Find the equation of the image of the line $y = x + 9$ when reflected in the $x$ -axis.

Solve the problem. -Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = - 4 x + 4$ .

Solve the problem. -Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = x + 2$ .

Solve the problem. -Find the image of the given figure under a 180° rotation about P.

Solve the problem. -Find the figure that results from reflecting the given figure across the line m, and then reflecting the result across line n.

Solve the problem. -If the given figure goes through a 90° clockwise rotation about P, followed by a 90° counterclockwise rotation of the resulting figure about Q, find the final image.

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

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

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, 6)

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) -( -2, 4)

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 the reflection that sends 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) -(3, 6)

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

Solve the problem. -A figure ABCDEF and its image A'B'C'D'E'F' after a rotation are given. Which point of the grid is the center of rotation?

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)

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.

For the given point, find the coordinates of the image point under a half-turn about the origin. -(2, -3)

Solve the problem. -A figure and its image under a rotation are given. Which point of the grid is the center of rotation?

Solve the problem. -Find the image of the given figure under a 90° counterclockwise rotation about P.

Solve the problem. -Find the equation of the image of the line y=x+9y = x + 9y=x+9 when reflected in the xxx -axis.

Solve the problem. -Find the equation of the line through (0,−8)( 0 , - 8 )(0,−8) and perpendicular to the line y=−4x+4y = - 4 x + 4y=−4x+4 .

Solve the problem. -Find the equation of the line through (0,−8)( 0 , - 8 )(0,−8) and perpendicular to the line y=x+2y = x + 2y=x+2 .

Solve the problem. -Find the image of the given figure under a 180° rotation about P.

Solve the problem. -Find the figure that results from reflecting the given figure across the line m, and then reflecting the result across line n.

Solve the problem. -If the given figure goes through a 90° clockwise rotation about P, followed by a 90° counterclockwise rotation of the resulting figure about Q, find the final image.

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

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

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

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

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

Solve the problem. -Find the equation of the image of the line $y = x + 9$ when reflected in the $x$ -axis.

Solve the problem. -Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = - 4 x + 4$ .

Solve the problem. -Find the equation of the line through $( 0 , - 8 )$ and perpendicular to the line $y = x + 2$ .