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(0, -3) ;  B(3, -2) and 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.

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

Solution : We have given

Vertices A(-3, 0), B(-2, 3), C(-1, 1)  is rotated 180° clockwise.

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

Then vertices would be

A(-3, 0) →→ A(3, 0)

B(-2, 3) →→ B(2, -3)

C(-1, 1) →→ C(1, -1).

Reflection y = -x then

A(0, -3) ;  B(3, -2) and C(-1, 1).

Therefore, A(0, -3) ;  B(3, -2) and C(1, -1).