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Question
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
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Solution
A (-3,5) , B(3,1), C(0,3), D(-1,-4)
Let A, B, C and D be the four vertices of the quadrilateral ABCD.
We know the distance between two points `P(x_1, y_1)` and `Q(x_2, y_2)` is given by distance formula:
`PQ = sqrt((x_2 - x_1)^2 + (y_2 - y^1)^2)`
Hence
`=> AB= sqrt((3 - (-3))^2 + (1 - (5))^2)`
`=> AB = sqrt((6)^2 + (4)^2)`
`=> AB = sqrt(36 + 16)`
`=> AB= sqrt52`
`=> AB = 2sqrt13`
Similarly,
`=> BC = sqrt((0 - 3)^2 + (3 - 1)^2)`
`=> BC = sqrt((-3)^2 + (2)^2)`
`=> BC = sqrt(9 + 4)`
`=> BC = sqrt(13)`
Similarly,
`CD = sqrt(((-1)-0)^2 + ((-4) - (3))^2)`
`=> CD = sqrt((-1)^2 + (-7)^2)`
`=> CD = sqrt(1 + 49)`
`=> CD = sqrt50`
`=>CD = 5sqrt2`
Also
`=> DA = sqrt((-1)-(-3)^2 + ((-4)-5)^2)`
`=> DA = sqrt((2)^2 + (-9)^2)`
`=> DA = sqrt85`
Hence from the above we see that it is not a quadrilateral.
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