Question

Show that the points (a, b), (a + 3,b + 4), (a - 1, b + 7) and (a - 4,b + 3) are the vertices of a parallelogram.​

Answer 1

Step-by-step explanation:

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ANSWER

Opposite sides of the parallelogram are parallel 

It means the slope of the two sides are equal

Slope of line passing through two points=x2−x1y2−y1

Consider, Sides AB and CD

∴ 3−16+2=5−310−2

28=28

Slope of AB= Slope of CD 

Slope of BC =(5−310−6)=24

Slope of AD =(3−12+2)=24

∴ The slope of BC=Slope of AD 

Opposite sides are parallel. It means it is a parallelogram.