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Show that the points A(1,2,3), B(-1,-2,-3),C(2,3,2),D(4,7,6) are the verticles of parallelogram ABCD,but it is not a rectangle |
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Answer» Step-by-step explanation: ANSWER Distance between A(1, 2, 3) and B(-1, -2, -1) is AB, =6 Distance between B(-1, -2, -1) and C(2, 3, 2) is BC,
Distance between C(2, 3, 2) and D(4, 7, 6) is CD, =6 The distance between A(1, 2, 3) and D(4, 7, 6) is AD,
Clearly, AB=CD and BC=AD Opposite sides are equal Now, we will find the length of diagonals The distance between A(1, 2, 3) and C(2, 3, 2) is AC,
Distance between B(-1, -2, -1) and D(4, 7, 6) is BD,
Clearly, AC =BD The diagonals are not equal, but opposite sides are equal Thus, Quadrilateral FORMED by ABCD is a parallelogram but not a rectangle |
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