Question

given A(2, 3), B(8, 7), C(6 1), which will make line AB perpendicular to line CD?D(9, 3)D(4, 4)D(3, 3)D(8, 4)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A(2, 3), B(8, 7), C(6 1)

Step 02:

Line AB

Slope formula

m = (y2 - y1) / (x2 - x1)

A (2 , 3) x1 = 2 y1 = 3

B (8 , 7) x2 = 8 y2 = 7

`m\text{ = }(7-3)/(8-2)=(4)/(6)=(2)/(3)`

Step 03:

Slope of the perpendicular line, m’

m' = -1 / m

`m\text{'}=\text{ }\frac{-1}{m\text{ }}=\text{ }\frac{-1\text{ }}{(2)/(3)}\text{ = -}(3)/(2)`

Step 04:

Line CD

m' = (y2 - y1) / (x2 - x1)

C (6 , 1) x1 = 6 y1 = 1

D ( x2, y2) x2 = x2 y2 = y2

`-(3)/(2)=\text{ }(y2-1)/(x2-6)`
`(3)/(2)=(1-y2)/(6-x2)`

We must test the numerical values to verify equality,

x2 = 9

y2 = 3

`(3)/(2)=(1-9)/(6-3)\text{ = }(-8)/(3)\text{ }`

x2 = 4

y2 = 4