Question

IL-
Prove that the line joining the points (1, 2) | 18
and (2, -2) is perpendicular to the line joining
(8, 2) and (4,1)​

Answer 1

Answer:

Step-by-step explanation:find first the gradient of both lines

Gradient of line joining (2,-2) and (1,2)

M=-4

Gradient of line joining (4,1) and (8,2)

M=1/4

-4 × 1/4 = -1

Therefore the lines are perpendicular because the product of their gradients is -1

Answer 2

Answer:

Step-by-step explanation:

Slopes of perpendicular lines are opposite reciprocals. So, if $m_{AB}$ × $m_{CD}$ = - 1, then AB ⊥ CD.

A(1, 2) , B(2, - 2)

$m_{AB}$ = $\frac{-2-2}{2-1}$ = - 4

C(8, 2), D(4, 1)

$m_{CD}$ = $\frac{2-1}{8-4}$ = $\frac{1}{4}$

$m_{AB}$ × $m_{CD}$ = - 4 × $\frac{1}{4}$ = - 1 ⇒ AB ⊥ CD