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

Answer:

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

Step-by-step 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 $T'(3,-1)$.