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?

Question

(–4, –3)
(–3, –4)
(3, 4)
(4, 3)

Answer 1

To find the location of point Q before the transformation, we need to understand the transformation rule given, which is R0, 90º. This means the rectangle is being rotated 90 degrees counterclockwise around the origin.

To reverse the 90-degree counterclockwise rotation, we need to rotate the point 90 degrees clockwise. The rule for rotating a point \((x, y)\) 90 degrees clockwise around the origin is given by the transformation:

\[ (x, y) \to (y, -x) \]

Now, we already have the coordinates for point Q' which is \(Q'(-3, 4)\). We will apply the inverse transformation to find the original coordinates of point Q before the rotation.

Substituting \(Q'(-3, 4)\) into the inverse transformation:

1. Identify \(x\) and \(y\):

   • \(x' = -3\)
   • \(y' = 4\)

2. Apply the transformation to find \(Q\): \[ Q(x, y) = (y', -x') \] \[ Q(-3, 4) = (4, -(-3)) = (4, 3) \]

Thus, the location of point Q before the transformation is:

\((4, 3)\)

So, the final answer is:

(4, 3)