Subjects geometry

Equidistant Locus

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Equidistant Locus


1. **State the problem:** Complete the sentence to describe the locus of points inside rectangle PQRS that are equidistant from sides PS and QR. 2. **Analyze the problem:** - The rectangle PQRS has corners P (top-left), Q (top-right), S (bottom-left), and R (bottom-right). - PS and QR are the left and right vertical sides of the rectangle. - Points equidistant from these two vertical sides lie on the vertical line exactly midway between them. 3. **Find the midpoints:** - The midpoint of PQ is halfway along the top edge. - The midpoint of RS is halfway along the bottom edge. 4. **Conclusion:** - The locus is the vertical line segment connecting the midpoints of PQ and RS. - This is because points on this line are equally distant from PS and QR. **Final answer:** The locus of points inside rectangle PQRS equidistant from sides PS and QR is a line between the midpoints of PQ and RS.