Question

A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?

(–4, –3)
(–3, –4)
(3, 4)
(4, 3)

Answer 1

To find the original location of the vertex Q before the transformation of the rectangle based on the rule \( R_0, 90^\circ \), we need to understand that a rotation of \( 90^\circ \) counterclockwise around the origin will transform a point \( (x, y) \) into \( (-y, x) \).

Given the new coordinates of the point Q' after rotation, which is \( Q'(-3, 4) \), we can apply the inverse transformation to find the original location of vertex Q.

The inverse transformation of \( (-y, x) \) is \( (y, -x) \).

Substituting the coordinates of Q':
- \( y = 4 \)
- \( x = -3 \)

Applying the inverse transformation:
\[
Q = (y, -x) = (4, -(-3)) = (4, 3)
\]

Thus, the location of Q before the transformation is \( (4, 3) \).

Among the provided options, the correct answer is:
**(4, 3)**.