Q. 134.6( 7 Votes )

# Using slopes. Prove that the points A(-2, -1), B(1,0), C(4, 3) and D(1, 2) are the vertices of a parallelogram.

Answer :

The property of parallelogram states that opposite sides are equal.

We have 4 sides as AB,BC,CD,DA

Given points are A(-2,-1),B(1,0),C(4,3) and D(1,2)

AB and CD are opposite sides, and BC and DA are the other two opposite sides.

So slopes of AB = CD and slopes BC = DA

Slope of AB =

The slope of BC =

The slope of CD =

Slope of DA =

Therefore the Slope of AB = Slope of CD and

The slope of BC = Slope of DA

Also, the product of slope of two adjacent sides is not equal to -1, therefore it is not a rectangle.

Hence ABCD is a parallelogram.

Rate this question :

By using the concept of slope, show that the points (– 2, – 1), (4, 0), (3, 3) and (– 3, 2) vertices of a parallelogram.

RD Sharma - MathematicsFind the value of x for which the points (x, – 1), (2, 1) and (4, 5) are collinear.

RD Sharma - MathematicsFind the angle between the X - axis and the line joining the points (3, – 1) and (4, – 2).

RD Sharma - MathematicsFind the angle between X - axis and the line joining the points (3, – 1) and (4, – 2).

RD Sharma - Mathematics