Question

Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Now, distance between A(4, 3) and B(6, 4), 

AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

AB = `sqrt((6 - 4)^2 + (4 - 3)^2`  

= `sqrt(2^2 + 1^2)`

= `sqrt(5)`

Distance between B(6, 4) and C(5, – 6),

BC = `sqrt((5 - 6)^2 + (-6 - 4)^2`

= `sqrt((-1)^2 + (-10)^2`

= `sqrt(1 + 100)`

= `sqrt(101)`

Distance between C(5, – 6) and D(– 3, 5),

CD = `sqrt((-3 - 5)^2 + (5 + 6)^2`

= `sqrt((-8)^2 + (11)^2`

= `sqrt(64 + 121)`

= `sqrt(185)`

Distance between D(– 3, 5) and A(4, 3),

DA = `sqrt((4 + 3)^2 + (3 - 5)^2`

= `sqrt(7^2 + (-2)^2`

= `sqrt(49 + 4)`

= `sqrt(53)`

In parallelogram, opposite sides are equal.

Here, we see that all sides AB, BC, CD and DA are different.

Hence, given vertices are not the vertices of a parallelogram.