Question

answer each question below.

(left image: figure b and figure a on a coordinate plane)
are figure a and figure b congruent?
● yes ○ no
which transformation will map figure a onto figure b exactly?
○ translate figure a to the right 6 units
○ translate figure a up 6 units
○ reflect figure a over the x - axis
○ reflect figure a over the y - axis
○ rotate figure a clockwise 90° about the origin
○ rotate figure a counterclockwise 180° about the origin
○ none of these

(right image: figure c and figure d on a coordinate plane)
are figure c and figure d congruent?
● yes ○ no
which transformation will map figure c onto figure d exactly?
○ translate figure c to the left 4 units
○ translate figure c down 4 units
○ reflect figure c over the x - axis
○ reflect figure c over the y - axis
○ rotate figure c clockwise 180° about the origin
○ rotate figure c counterclockwise 90° about the origin
○ none of these

Explanation:

First Sub - Question (Figure A and Figure B)

To determine the transformation from Figure A to Figure B, we analyze the position and orientation. A reflection over the \(y\) - axis would map the right - side figure (Figure A) to the left - side figure (Figure B) as the \(y\) - axis is the vertical line of symmetry here. Translating right 6 units would move Figure A further right, translating up 6 units would move it up, reflecting over the \(x\) - axis would flip it vertically, rotating \(90^{\circ}\) clockwise or \(180^{\circ}\) counter - clockwise would change the orientation in a way that doesn't match Figure B.

To map Figure C to Figure D, a reflection over the \(x\) - axis would flip Figure C (which is above the \(x\) - axis) to the position of Figure D (which is below the \(x\) - axis) with the same shape and size. Translating left 4 units or down 4 units would not give the correct orientation, reflecting over the \(y\) - axis would move it horizontally, rotating \(180^{\circ}\) or \(90^{\circ}\) counter - clockwise would change the orientation in an incorrect way.

Answer:

Reflect Figure A over the \(y\) - axis

Second Sub - Question (Figure C and Figure D)