Question

How to do question 24. a and b?

Answer 1

a) Equation of BC is `color(blue)(3y - x = 22)`

b) Coordinates of `color(green)(C (14, 12)`

Explanation:

`A (4,2), B (2,8)`

Equation of AC `color(blue)(y = x - 2)`

a) To find equation of BC#

Slope of AB = (8-2) / (2 - 4) = -3#

Slope of BC = -1 / (-3) = 1/3#

Equation of BC

`y - 8 = (1/3) (x - 2)`

`3y - 24 = x - 2`

Equation of BC is `color(blue)(3y - x = 22)`

b) To find the coordinates of C.

This can be arrived at by solving equations of AC and BC.

Equation of AC `y - x = -2` Eqn (1)

Equation of BC `3y - x = 22` Eqn (2)

Subtracting Eqn (1) from (2),

`3y - y = 22 - (-2)`

`y = 24 / 2 = 12`

Substituting value of y in equation (1),

`12 - x = -2`

`x = 12 + 2 = 14`

Coordinates of `color(green)(C (14, 12)`