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 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 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

Answer 1

To determine the new positions of the vertices \( P \) and \( R \) after the rotation of vertex \( Q \) from \( Q(-4, -9) \) to \( Q'(-9, 4) \), we can follow the rotation operation.

The transformation can be inferred to be a 90-degree counterclockwise rotation around the origin. The general rule for a 90-degree counterclockwise rotation of a point \( (x, y) \) is given by:
\[
(x, y) \to (-y, x)
\]

### Step 1: Apply the transformation to point \( P(-4, 0) \)
Using the rotation rule:
\[
P(-4, 0) \to (-0, -4) = (0, -4)
\]
So, \( P' \) will be \( (0, -4) \).

### Step 2: Apply the transformation to point \( R(4, -4) \)
Using the rotation rule:
\[
R(4, -4) \to (4, -4) \to (4, -4) = (4, 4)
\]
So, \( R' \) will be \( (-4, 4) \).

Based on our calculations, the coordinates after rotation are:
- \( P' = (0, -4) \)
- \( R' = (-4, 4) \)

### Conclusion:
Thus, the image of the points after rotation is:
- \( P' \) is at \( (0, -4) \)
- \( R' \) is at \( (-4, 4) \)

The correct response from the options would be:
**P′(0,−4) and R′(−4,4)**.