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Question
Show that the following points taken in order to form the vertices of a parallelogram
A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)
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Solution
AB = `sqrt((5 + 7)^2 + (10 + 3)^2`
= `sqrt((12)^2 + (13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`
BC = `sqrt((15 - 5)^2 + (8 - 10)^2`
= `sqrt(10^2 + (-2)^2`
= `sqrt(100 + 4)`
= `sqrt(104)`
CD = `sqrt((3 - 15)^2 + (-5 - 8)^2`
= `sqrt((-12)^2 + (- 13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`
AD = `sqrt((3 + 7)^2 + (-5 + 3)^2`
= `sqrt((10)^2 + (-2)^2`
= `sqrt(100 + 4)`
= `sqrt(104)`
AB = CD = `sqrt(313)` and BC = AD = `sqrt(104)` ...(Opposite sides are equal)
∴ ABCD is a parallelogram.
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