Question

Rectangle PQRS
has vertices Q(4,−2)
and S(−1,3)
. What are the coordinates of vertices P
and R
? Note, the vertex labels are located counterclockwise on the graph.

Answer 1

To find the coordinates of vertices P and R in rectangle PQRS, we can use the information given about vertices Q and S, and the properties of rectangles.

1. **Understanding the positions of Q and S:**
- The coordinates of Q are \( Q(4, -2) \).
- The coordinates of S are \( S(-1, 3) \).
- Since the rectangle is labeled counterclockwise, \( Q \) and \( S \) are adjacent vertices.

2. **Finding the coordinates of vertices P and R:**
- The vertices of a rectangle are defined such that opposite sides are parallel and equal in length.
- The coordinates for R will correspond to Q along the same line (horizontal or vertical) as S, and coordinates for P will correspond to S along the same line as Q.

3. **Finding P:**
- Since Q and S share a vertical line, we can maintain the x-coordinate of S with the y-coordinate of Q to find P.
- Therefore, the coordinates of P are:
\[
P = (x_q, y_s) = (4, 3)
\]

4. **Finding R:**
- Similarly, since Q and S share a horizontal line, we can maintain the y-coordinate of S with the x-coordinate of Q to find R.
- Therefore, the coordinates of R are:
\[
R = (x_s, y_q) = (-1, -2)
\]

5. **Final Coordinates:**
- The coordinates of vertices P and R are:
- \( P(4, 3) \)
- \( R(-1, -2) \)

To summarize, the positions are:
- \( P(4, 3) \)
- \( R(-1, -2) \)