Question

Triangle RST has vertices R(−2, 2), S(1, 1), and T(−1, −3). Find the coordinates for the image of each vertex for the given rotation.

R(90°, 0) (triangle RST)

A.
R'(−2, −2), S'(−1, 1), and T'(3, −1)
B.
R'(−2, 2), S'(1, −2), and T'(3, 1)
C.
R'(2, 2), S'(−1, −1), and T'(1, −3)
D.
R'(−2, 2), S'(1, −1), and T'(3, 1)

Answer 1

A.
`R'(-2,-2),S'(-1,1),` and
`T'(3,-1)`

Explanation:

Given:

Vertices of triangle RST are
`R(-2,2),S(1,1),` and
`T(-1,-3)`.

Rotation is 90° about the center O(0,0). The rotation is counter-clockwise as the angle of rotation is positive.

Now, the co-ordinate rule for 90° rotation counter-clockwise is given as:
`(x,y)` →
`(-y,x)`

`x` and
`y` values interchange their places with
`y` becoming negative when interchanged.

So,
`R(-2,2)` →
`R'(-2,-2)`

`S(1,1)` →
`S'(-1,1)`

`T(-1,-3)` →
`T'(-(-3),-1)`

⇒
`T(-1,-3)` →
`T'(3,-1)`

Therefore, the image of the vertices are
`R'(-2,-2),S'(-1,1),` and
`T'(3,-1)`.