Question

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find:

1. The equation of the line.
2. The co-ordinates of A and B.
3. The co-ordinates of M.

Answer 1

i. Slope of PQ =`(-2 - 4)/(5 + 1) = (-6)/6 = -1`

Equation of the line PQ is given by

y – y₁ = m(x – x₁)

y − 4 = −1(x + 1)

y − 4 = −x − 1

x + y = 4 − 1

x + y = 3

ii. For point A (on x-axis), y = 0.

Putting y = 0 in the equation of PQ, we get,

x = 3

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

For point B (on y-axis), x = 0.

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

y = 3

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

iii. M is the mid-point of AB.

So, the co-ordinates of point M are

`( (3 + 0)/2 , (0 + 3)/2) = (3/2, 3/2)`