Question

52. 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

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=

x

2

−x

1

y

2

−y

1

Consider, Sides AB and CD

∴

3−1

6+2

=

5−3

10−2

2

8

=

2

8

Slope of AB= Slope of CD

Slope of BC =(

5−3

10−6

)=

2

4

Slope of AD =(

3−1

2+2

)=

2

4

∴ The slope of BC=Slope of AD

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