Verify that quadrilateral BCDE is a rhombus with vertices B(-5, 1), C(0, 6), D(5, 1) and E (0, -4) by showing that all four sides are equal.

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14-10-2016
Mathematics

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Verify that quadrilateral BCDE is a rhombus with vertices B(-5, 1), C(0, 6), D(5, 1) and E (0, -4) by showing that all four sides are equal.

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apologiabiology apologiabiology · Answer 1 · 2016-10-14T20:59:16+02:00

apologiabiology apologiabiology

14-10-2016

find the distance between each

between points (x1,y1) and (x2,y2)
D=[tex] \sqrt{(x2-x1)^2+(y2-y1)^2} [/tex]

find and verify that
BC=CD=DE=EB

so
BC=[tex] \sqrt{(0-(-5))^2+(6-1)^2} [/tex]=5√2
CD=[tex] \sqrt{(5-0)^2+(1-6)^2} [/tex]=5√2
DE=[tex] \sqrt{(-4-1)^2+(0-5)^2} [/tex]=5√2
EB=[tex] \sqrt{(-5-0)^2+(1-(-4))^2} [/tex]=5√2

true

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