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)

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

Step-by-step 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).

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