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)

Question

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Respuesta :

DarcySea DarcySea · Answer 1 · 2019-11-06T02:25:35+01:00

Answer:

A. [tex]R'(-2,-2),S'(-1,1),[/tex] and [tex]T'(3,-1)[/tex]

Step-by-step explanation:

Given:

Vertices of triangle RST are [tex]R(-2,2),S(1,1),[/tex] and [tex]T(-1,-3)[/tex].

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:[tex](x,y)[/tex] → [tex](-y,x)[/tex]

[tex]x[/tex] and [tex]y[/tex] values interchange their places with [tex]y[/tex] becoming negative when interchanged.

So, [tex]R(-2,2)[/tex] → [tex]R'(-2,-2)[/tex]

[tex]S(1,1)[/tex] → [tex]S'(-1,1)[/tex]

[tex]T(-1,-3)[/tex] → [tex]T'(-(-3),-1)[/tex]

⇒[tex]T(-1,-3)[/tex] → [tex]T'(3,-1) [/tex]

Therefore, the image of the vertices are [tex]R'(-2,-2),S'(-1,1),[/tex] and [tex]T'(3,-1)[/tex].