Question

ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?

A) A'(0, 3), B'(2, 3), C'(1, 1)



B) A'(0, -3), B'(3, -2), C'(1, -1)



C) A'(-3, 0), B'(-3, 2), C'(-1, 1)



D) A'(0, -3), B'(-2, -3), C'(-1, -1)

Answer 1

i would have to go with B

Answer 2

B)The coordinate become A' (0, -3) , B'(3, -2) , C'(1, -1).

Explanation:

Given: ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x.

To find: What are the coordinates of the vertices of the image.

Solution: We have given that vertices A(-3, 0), B(-2, 3), C(-1, 1).

By the transformation rule of 180° : ( x, y )→→ (-x, -y).

A(-3, 0) →→A' (3, 0).

B(-2, 3) →→ B'(2, -3).

C(-1, 1) →→ C'(1, -1).

Now , By apply the reflection across the line y = -x.

( x, y )→→ (-y, -x)

Now the parents function are A' (3, 0) , B'(2, -3) , C'(1, -1).

The coordinate become A' (0, -3) , B'(3, -2) , C'(1, -1).

Therefore , B)The coordinate become A' (0, -3) , B'(3, -2) , C'(1, -1).