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?

The coordinates of the vertices of the image are:

A"(0,-3) , B"(3,-2) and C"(1,-1)

Step-by-step explanation:

We know that if any point is rotated by 180° clockwise then the rule that holds this transformation is:

(x,y) → (-x,-y)

and also the rule that holds for the reflection of a point about the line y= -x is:

(x,y) → (-y,-x)

Hence, now when ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin the transformed  vertices are given by:

A(-3,0) → A'(3,0)

B(-2,3) → B'(2,-3)

C(-1,1) → C'(1,-1)

Also now when it is reflected across the line y=-x the points of the resulting image is:

A'(3,0) → A"(0,-3)

B'(2,-3) → B"(3,-2)

C'(1,-1) → C"(1,-1)

Hence,

A(-3,0) → A"(0,-3)

B(-2,3) → B"(3,-2)

C(-1,1) → C''(1,-1)