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ABCD is a rectangle formed by the points...

ABCD is a rectangle formed by the points `A(1,\ 1),``B(1,\ 4),`` C(5,\ 4)` and `D(5,\ 1)`. P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? A rectangle? or a rhombus? Justify your answer.

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To determine whether the quadrilateral PQRS is a square, rectangle, or rhombus, we will follow these steps: ### Step 1: Find the midpoints P, Q, R, and S 1. **Midpoint P (of AB)**: - A(1, 1) and B(1, 4) - \( P = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + 1}{2}, \frac{1 + 4}{2} \right) = \left( 1, \frac{5}{2} \right) \) ...
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