The coordinates of PQR are P(1, 1), Q(2, 2), and R(3, 1). If PQR is rotated 90° about the origin, what are the vertices of P'Q'R
'?
1 answer:
Answer:
(-1, 1), (-2, 2), and (-1, 3)
Step-by-step explanation:
The formula for rotation of a point (x,y) by an angle θ about the origin is
x' = xcosθ - ysinθ
y' = ycosθ + xsinθ
If θ = 90°, sinθ = 1 and cosθ = 0, and the formula becomes
x' = -y
y' = x
P: (1, 1) ⟶ (-1, 1)
Q:(2, 2) ⟶ (-2, 2)
R: (3, 1) ⟶ (-1, 3)
The vertices of P'Q'R' are (-1, 1), (-2, 2), and (-1, 3).
The Figure below shows the triangle before and after the rotation.
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