Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(−1, 7, 8), C(1, 10, 1), D(3, 4, −4)
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Step 1
Calculate midpoint of AC: \[ M_{AC} = \left(\frac{1+1}{2}, \frac{1+10}{2}, \frac{3+1}{2}\right) = (1, 5.5, 2) \] Calculate midpoint of BD: \[ M_{BD} = \left(\frac{-1+3}{2}, \frac{7+4}{2}, \frac{8+(-4)}{2}\right) = (1, 5.5, 2) \] Since \(M_{AC} = M_{BD}\), the Show more…
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