Quadrilateral ABCD has vertices A(−5, 0), B(0, 3), C(5, 0), and D(0, −3). Use the grid to plot...

Question

Quadrilateral ABCD has vertices A(−5, 0), B(0, 3), C(5, 0), and D(0, −3).
Use the grid to plot quadrilateral ABCD.
(a). Use the distance formula to verify AB ≅ CD and BC ≅ DA.
(b). Calculate and label the midpoint of each side using coordinate notation: M on AB, N on BC, P on CD, and Q on DA.
(c). Classify the polygon formed by connecting M, N, P, and Q in order. Verify your classification.
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SnapAndSolve AI · Accepted Answer

Plot ABCD: Plot A(−5, 0), B(0, 3), C(5, 0), and D(0, −3), then connect A → B → C → D → A. (a) Using d = √[(x₂ − x₁)² + (y₂ − y₁)²]: AB = √[(0 + 5)² + (3 − 0)²] = √34.CD = √[(0 − 5)² + (−3 − 0)²] = √34.BC = √[(5 − 0)² + (0 − 3)²] = √34.DA = √[(−5 − 0)² + (0 + 3)²] = √34. Thus AB ≅ CD and BC ≅ DA. (b) Using the midpoint formula ((x₁ + x₂)/2, (y₁ + y₂)/2): M = ((−5 + 0)/2, (0 + 3)/2) = (−5/2, 3/2).N = ((0 + 5)/2, (3 + 0)/2) = (5/2, 3/2).P = ((5 + 0)/2, (0 − 3)/2) = (5/2, −3/2).Q = ((0 − 5)/2, (−3 + 0)/2) = (−5/2, −3/2). (c) MNPQ is a rectangle, not a square. MN and PQ are horizontal, while NP and QM are vertical. Therefore opposite sides are parallel and all four angles are right angles. Also, MN = PQ = 5 and NP = QM = 3. Since adjacent side lengths differ, it is not a square.

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Quadrilateral ABCD has vertices A(−5, 0), B(0, 3), C(5, 0), and D(0, −3). Use the grid to plot...

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