Question

The line on the graph passes through the points A (1, 3) and B (7, 1).

YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
+
A
D
c) Find the equation of the line passing
through point (4, 2) and perpendicular
to AB.

Answer 1

Explanation:

a) gradient of AB

or

Slope of AB

`Slope , m = (y_B - y_A)/(x_B - x_A)`

`=(1 - 3 )/(7 - 1 ) \\\\=(-2)/(6)\\\\=-(1)/(3)`

b)

when lines are perpendicular to each other, the product of their slope = - 1

That is ,

`m_(AB) * m_(perpendicular) = - 1 \\\\- (1)/(3) * m_(perpendicular) = - 1\\\\m_(perpendicular) = - 1 * (-3)/(1) = 3`

c) Equation of the line perpendicular to line AB and passing through ( 4 , 2 )

`( y - y_1) = m_(perpendicular) ( x - x_1) \ where \ (x_1 , y_ 1 ) = ( 4 , 2 ) \\\\( y - 2 ) = 3(x - 4 ) \\\\y = 3x - 12 + 2\\\\y = 3x - 10`