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.
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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.
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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.
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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: \[ P = (x_q, y_s) = (4, 3) \]
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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: \[ R = (x_s, y_q) = (-1, -2) \]
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Final Coordinates:
- The coordinates of vertices P and R are:
- \( P(4, 3) \)
- \( R(-1, -2) \)
- The coordinates of vertices P and R are:
To summarize, the positions are:
- \( P(4, 3) \)
- \( R(-1, -2) \)