Question

the points A (4,-2),B (7,2),C (6,9), and D (-4,-6) form a parallelogram. find the length of the altitude of the parallelogram on the base AB

Answer 1

Answer:

Length of the altitude of parallelogram on the base AB is 5 units.

Step-by-step explanation:

Given points A ( 4, -2) and B (7, 2)

Equation of the line AB is given by

y + 2/x - 4 = 2 + 2/7 - 4

=> y + 2/x - 4 = 4/3

=> 3y + 6 = 4x - 16

=> 4x - 3y - 22 = 0

Length of the altitude of parallelogram is same as the perpendicular

distance from either C ( 6, 9) or D(-4, -6) to the base AB

Thus, length of altitude

=   | 4*6 - 3*9 - 22|/√4² + 3²

=  | 24 - 27 - 22|/5

=  |-25|/5

= 5 units.

Hence length of the altitude of parallelogram on the base AB is 5 units.

Hope, it helps !