Question

Show that the points A (1,- 2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Answer 1

Here to prove that above mentioned points are the vertices of a parallelogram, we have to focus on the properties of a parallelogram.

Explanation:

So what we have here:-

A = (1,-2)

B = (3, 6)

C = (5, 10)

D = (3, 2)

AB and CD are opposite sides.

So if opposite sides are equal then it is a parallelogram.

A = (1, -2)

B = (3, 6)

Length of AB =length along the x-axis = 3 – 1 = 2.

C = (5, 10)

D = (3, 2)

Length of CD = length along x –axis = 5 – 3 = 2.

As AB = CD so they are of equal length.

Now for AD and BC

Length of BC = length along y axis = 10 – 6 = 4.

Length of AD = length along y-axis = 2 – (-2) = 2 + 2 = 4.

As BC = AD so opposite sides are equal length.  

As opposite sides are of equal length so the points are the vertices of a parallelogram.

Answer 2

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