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Question
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
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Solution
Let the points (−3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices A, B, C, and D of the given quadrilateral respectively.
AB = `sqrt((-3,-3)^2 + (5-1)^2)`
= `sqrt((-6)^2+(4)^2)`
= `sqrt(36+16)`
= `sqrt(52)`
= `2sqrt13`
BC = `sqrt((3-0)^2+(1-3)^2)`
= `sqrt((3)^2+(-2)^2)`
= `sqrt(9+4)`
= `sqrt13`
CD = `sqrt((0-(-1))^2+(3-(-4))^2)`
= `sqrt((1)^2+(7)^2)`
= `sqrt(1+49)`
= `sqrt50`
= `5sqrt2`
AD = `sqrt((-3-(-1))^2+(5-(-4))^2)`
= `sqrt((-2)^2+ (9)^2)`
= `sqrt(4+81)`
= `sqrt85`
AC = `sqrt ([0 - (-3)^2] + (3 - 5)^2)`
= `sqrt ((3)^2 + (-2)^2)`
= `sqrt (9 + 4)`
= `sqrt13`
BD = `sqrt ((-1 - 3)^2 + (-4 - 1)^1)`
= `sqrt ((-4)^2 + (5)^2)`
= `sqrt (16 + 25)`
= `sqrt41`
It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc.
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