Question

joseph makes a design on a coordinate grid. he draws figure a and then draws figure b.
which sequence of transformations can joseph perform to show that figure a and figure b are congruent?
rotate figure a clockwise 90° about the origin and then
translate figure a 4 units right and then reflect the image across the x - axis.
reflect figure a across the y - axis and then translate the image 4 units right.
rotate figure a clockwise 90° about the origin and then translate the image 2 units down.

Explanation:

Step1: Analyze each option

• Option1: Translate figure A 4 units right and then reflect the image across the x - axis
• Translating figure A 4 units right moves it horizontally. Then reflecting across the x - axis flips it vertically. This does not match the position of figure B.
• Option2: Reflect figure A across the y - axis and then translate the image 4 units right
• Reflecting across the y - axis flips figure A horizontally. Translating 4 units right after that does not result in figure B.
• Option3: Rotate figure A clockwise \(90^{\circ}\) about the origin and then translate the image 2 units down
• Rotating figure A clockwise \(90^{\circ}\) about the origin changes its orientation. Translating 2 units down after rotation does not match figure B.
• Option4: Rotate figure A clockwise \(90^{\circ}\) about the origin
• When we rotate figure A clockwise \(90^{\circ}\) about the origin, we can observe that it will match the position of figure B.

Answer:

Rotate figure A clockwise \(90^{\circ}\) about the origin.