Question

The co-ordinates of two points A and B are (–3, 4) and (2, –1). Find:

1. the equation of AB;
2. the co-ordinates of the point where the line AB intersects the y-axis.

Answer 1

i. Given, co-ordinates of two points A and B are (–3, 4) and (2, –1).

Slope = `(-1 - 4)/(2 + 3) = (-5)/5 = -1`

The equation of the line AB is given by:

y − y₁ = m(x − x₁)

y + 1 = −1(x − 2)

y + 1 = −x + 2

x + y = 1

ii. Let the line AB intersects the y-axis at point (0, y).

Putting x = 0 in the equation of the line, we get,

0 + y = 1

y = 1

Thus, the co-ordinates of the point where the line AB intersects the y-axis are (0, 1).