The points A(4,-2) B(7,2) C(0,9) and D(-3,5) form a parallelogram. Find the leng...

Questions

August 2021 2 33 Report

The points A(4,-2) B(7,2) C(0,9) and D(-3,5) form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.

siddhartharao77

Verified answer

Given A(4,-2) B(7,2) C(0,9) and D(-3,5).

Area of the triangle ABC = 1/2 (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)

= 1/2(4(2-9) + 7(9+2)

= 49/2.

Area of parallellogram = 2 * 49/2 = 49 square units.

Base of the parallelogram AB = root(x1 - x2)^2 + (y1 - y2)^2

= root (4 - 7)^2 + (-2-2)^2

= root 9 + 16

= root 25

= 5.

The height of the parallelogram = 49/5.