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

Answer:

Step-by-step explanation:

a) gradient of AB

  or

  Slope of AB

  $Slope , m = \frac{y_B - y_A}{x_B - x_A}$

               $=\frac{1 - 3 }{7 - 1 } \\\\=\frac{-2}{6}\\\\=-\frac{1}{3}$

b)

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

That is ,

           $m_{AB} \times m_{perpendicular} = - 1 \\\\- \frac{1}{3} \times m_{perpendicular} = - 1\\\\m_{perpendicular} = - 1 \times \frac{-3}{1} = 3$

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

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