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)

Question

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 $Q^{\prime }(-9,4)$, 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, $P^{\prime }$ 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, $R^{\prime }$ will be $(-4,4)$.

Based on our calculations, the coordinates after rotation are:

• $P^{\prime }=(0,-4)$
• $R^{\prime }=(-4,4)$

Conclusion:

Thus, the image of the points after rotation is:

• $P^{\prime }$ is at $(0,-4)$
• $R^{\prime }$ is at $(-4,4)$

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