Question

show tha A(-4,-7) B(-1,2) C(8,5) & D(5,-4) are the vertices of parallelogram,( in slope​)

Answer 1

Step-by-step explanation:

A(-4,-7) B(-1,2) C(8,5) & D(5,-4)

For AB

A(-4,-7) B(-1,2)

x1, y1. x2, y2

$slope = y2 - y1 \div x2 - x1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 - ( - 7) \div ( - 1) - ( - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 + 7 \div ( - 1) + 4 \\ \: \: \: \: \: \: \: \: \: \: \: \: = 9 \div 3 \\ slope \: of \: ab = 3$

For BC

B(-1,2) C(8,5)

x1, y1. x2, y2

Using slope formula as same as above we get,

Slope of BC =1/3

For CD

C(8,5) D(5,-4)

x1, y1 x2, y2

Using slope formula as same as above we get,

Using slope formula as same as above we get, Slope of CD =3

For AD

A(-4,-7) D(5,-4)

x1, y1. x2, y2

Using slope formula as same as above we get,

Using slope formula as same as above we get, Slope of AD = 1/3

If slopes are equal then lines are parallel

AB=CD

Therefore AB ll CD

BC=AD

THEREFORE BC ll AD

If opposite sides of quadrilateral are parallel then it is parallelogram

Therefore quadrilateral ABCD IS Parallelogram

Therefore,

A(-4,-7) B(-1,2) C(8,5) & D(5,-4) are the vertices of parallelogram,

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