The vertices of triangle qpr are q(–4,0), p(–6, 7), and r(–2, 1). / is rotated 90° counterclockwise about the origin to form q' p' r'. what are the coordinates of the vertices of q'p'r'?
a. q’(0, –4), p’(–7, –6), r’(–1, –2)
b. q’(0, –4), p’(7, 6), r’(1, –2)
c. q’(0, 4), p'(–7, 6), r’(–1, 2)
d. q’(4, 0), p’(6, 7), r’(2, –1)

 The correct option is

(A)  Q'(0,-4), P'(–7, -6) and R'(–1, -2).

Step-by-step explanation:  Given that the vertices of triangle QPR are Q(–4,0), P(–6, 7), and R(–2, 1). The triangle is rotated 90° counterclockwise about the origin to form Q' P' R'.

We are to find the co-ordinates of the vertices of triangle Q'P'R'.

We know that

if a point (x, y) is rotated 90° counterclockwise about the origin, then its co-ordinates becomes

(x, y)  ⇒  (-y, x).

So, the vertices of triangle QPR changes as follows :

Q(-4, 0) ⇒ Q' (0, -4),

P(-6,7)   ⇒  P'(-7, -6)

and

R(-2, 1)   ⇒  R'(-1, -2).

Thus, the co-ordinates of the vertices of triangle Q'P'R' are Q'(0,-4), P'(–7, -6) and R'(–1, -2).

Option (A) is CORRECT.

sine

step-by-step explanation: