Question

4) Prove that the set of co-ordinatee are the vertices
of parallelogram. (-5,3) (1,-11) (7,-6) (1,2)
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Answer 1

$\large\bf{\underline\orange{Answer \:↝}}$

Que :- Prove that each of the set of co-ordinates are the vertices of parallelograms. (−5,−3),(1,−11),(7,−6),(1,2)

Ans :-

$d = \sqrt{ ({x_{2} - x_{1})}^{2} + ({y_{2} - y_{1})}^{2} }$

$AB = \sqrt{ {( - 5 - 1)}^{2} + {( - 3 + 11)}^{2} }$

$= \sqrt{ {( 6)}^{2} + {(8)}^{2} }$

$= \sqrt{100}$

AB = 10

$BC = \sqrt{ {(1 - 7)}^{2} + {( - 11 - ( - 6))}^{2} }$

$= \sqrt{ {( - 6)}^{2} + {( - 5)}^{2} }$

$= \sqrt{61}$

BC = √61

$CD = \sqrt{ {(7 - 1}^{2} + {( - 6 - 2)}^{2} }$

$= \sqrt{ {(6)}^{2} + {( - 8)}^{2} }$

$= \sqrt{100}$

CD = 10

$DA = \sqrt{ {(1 + 5)}^{2} + {(2 + 3)}^{2} }$

$= \sqrt{ {(6)}^{2} + {(5)}^{2} }$

$= \sqrt{61}$

DA = √61

∴ AD = BC and AB = CD

∴ Given vertices from a llgm.