Question

A vertex of △PQR is rotated from Q(−4,−9) to Q′(−9,4) . Use rotation function mapping to determine where the image of the other two vertices P(−4,0) and R(4,−4) , should be placed.(1 point) Responses P′(0,−4) and R′(−4,4) upper P prime left parenthesis 0 comma negative 4 right parenthesis and upper R left parenthesis negative 4 comma 4 right parenthesis P′(0,4) and R′(−4,−4) upper P prime left parenthesis 0 comma 4 right parenthesis and upper R left parenthesis negative 4 comma negative 4 right parenthesis P′(0,−4) and R′(−4,−4) upper P prime left parenthesis 0 comma negative 4 right parenthesis and upper R left parenthesis negative 4 comma negative 4 right parenthesis P′(0,4) and R′(−4,4)

Answer 1

To determine the new positions of the vertices P and R after the rotation that moves Q to Q', we can analyze the transformation in terms of rotation.

Given:

• Original point Q: \((-4, -9)\)
• Rotated point Q': \((-9, 4)\)

Let's first find the angle of rotation. The transformation appears to be a 90-degree rotation counter-clockwise around the origin (0, 0), since:

• The vector from the origin to Q is \((-4, -9)\).
• A 90-degree counter-clockwise rotation of Q \((-4, -9)\) to \((-9, 4)\) can be seen as swapping the coordinates and changing the sign of the new x-coordinate.

Now, let's apply the same rotation to the other points P and R.

1. For point P: \((-4, 0)\)

   • After a 90-degree counter-clockwise rotation, the transformation is as follows: \[ P' = (x, y) \rightarrow (-y, x) \] Thus, \[ P' = (0, -4) \]

2. For point R: \((4, -4)\)

   • Also using the same transformation, \[ R' = (x, y) \rightarrow (-y, x) \] Therefore, \[ R' = (4, -4) \rightarrow (4, 4) \]

Putting it all together, we have:

• \(P' = (0, -4)\)
• \(R' = (-4, 4)\)

Thus, the correct response is: P′(0,−4) and R′(−4,4).