Question

Without using the distance formula, show that the points A(4, 5), B(1, 2), C(4, 3) and D(7, 6) are the vertices of a parallelogram.

Answer 1

The given points are A(4, 5), B(1, 2), C(4, 3) and D(7, 6).

Slope of AB = `(2 - 5)/(1 - 4)`

Slope of AB = `(-3)/(-3)`

Slope of AB = 1

Slope of CD = `(6 - 3)/(7 - 4)`

Slope of CD = `3/3`

Slope of CD = 1

Since, slope of AB = slope of CD

Therefore, AB || CD

Slope of BC = `(3 - 2)/(4 - 1) = 1/3`

Slope of DA = `(5 - 6)/(4 - 7) = (-1)/(-3) = 1/3`

Since, slope of BC = slope of DA

Therefore, BC || DA

Hence, ABCD is a parallelogram.