Question

solve the problems.
1 in the diagram, figures a and a are congruent. which sequence of transformations can be performed on figure a to show that the figures are congruent?
a translate figure a 7 units right. then reflect figure a across the x - axis.
b translate figure a 5 units down. then translate figure a 7 units to the right.
c reflect figure a across the y - axis. then translate figure a 5 units down.
d rotate figure a 90° counterclockwise around the origin. then reflect figure a across the x - axis.
2 in the diagram, △qrs≅△tuv. which sequences of transformations can be performed on △qrs to show that the triangles are congruent? choose all the correct answers.
a reflect △qrs across the x - axis. then reflect the image across the y - axis. then reflect the image across the x - axis.
b reflect △qrs across the y - axis.
c rotate △qrs 90° clockwise around the origin. then reflect the image across the y - axis.
d rotate △qrs 180° around the origin. then reflect the image across the x - axis.
e translate △qrs 4 units to the left.

Explanation:

Step1: Analyze option A for first problem

Check if translation and reflection work. Translating figure A 7 units right moves it horizontally. Reflecting across x - axis flips it over x - axis. This makes figure A congruent to A''.

Step2: Analyze option B for first problem

Two translations don't result in correct orientation. Translating 5 units down and then 7 units right doesn't match orientation of A''.

Step3: Analyze option C for first problem

Reflecting across y - axis and translating 5 units down doesn't match orientation of A''.

Step4: Analyze option D for first problem

Rotating 90° counter - clockwise and reflecting across x - axis doesn't match orientation of A''.

Step5: Analyze option A for second problem

Reflecting across x - axis, then y - axis and then x - axis again can map △QRS to △TUV.

Step6: Analyze option B for second problem

Reflecting across y - axis can map △QRS to △TUV.

Step7: Analyze option C for second problem

Rotating 90° clockwise and reflecting across y - axis doesn't map △QRS to △TUV.

Step8: Analyze option D for second problem

Rotating 180° and reflecting across x - axis doesn't map △QRS to △TUV.

Step9: Analyze option E for second problem

Translating 4 units left doesn't map △QRS to △TUV.

Answer:

1. A. Translate figure A 7 units right. Then reflect figure A' across the x - axis.
2. A. Reflect △QRS across the x - axis. Then reflect the image across the y - axis. Then reflect the image across the x - axis.; B. Reflect △QRS across the y - axis.