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?

Answer 1

B(-2,3) because its reflected of the line of y=-x

I hope this helps you :)

Answer 2

The coordinates of the vertices of the image are:

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

Explanation:

If the graph or a figure is rotated 180 degree clockwise or anticlockwise then the change in the coordinates of each of the point of the figure is:

(x,y) → (-x,-y)

Hence, here if ΔABC is rotated 180° clockwise about the origin then the change in coordinates is:

A(-3,0) → A'(3,0)

B(-2,3) → B'(2,-3)

C(-1,1) → C'(1,-1)

and now when it is reflected across the line y= -x then the change in coordinates or the rule is given by:

(x,y) → (-y,-x)

Hence, we get:

A'(3,0) → A''(0,-3)

B'(2,-3) → B''(3,-2)

and C'(-1,1) → C''(1,-1)