Question

The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC. If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the co-ordinates of P and Q.

Answer 1

For the line AB:

Slope of AB = m = `(2 - 0) /(2 - 4) = 2/(-2)= -1 `

(x₁, y₁) = (4, 0)

Equation of the line AB is

y − y₁ = m(x − x₁)

y − 0 = −1(x − 4)

y = −x + 4

x + y = 4     ...(1)

For the line BC:

Slope of BC = m = `(6 - 2)/(0 - 2) = 4/(-2) = -2`

(x₁, y₁₎ = (2, 2)

Equation of the line BC is

y − y₁ = m(x − x₁)

y − 2 = −2(x − 2)

y − 2 = −2x + 4

2x + y = 6     ...(2)

Given that AB cuts the y-axis at P.

So, the abscissa of point P is 0.

Putting x = 0 in (1), we get,

y = 4

Thus, the co-ordinates of point P are (0, 4).

Given that BC cuts the x-axis at Q.

So, the ordinate of point Q is 0.

Putting y = 0 in (2), we get,

2x = 6

`=>` x = 3

Thus, the co-ordinates of point Q are (3, 0).