Question

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

(i) The equation of the line.

(ii) The co-ordinates of A and B.

(iii) The co-ordinates of M.

Answer 1

(i) Slope of PQ =

Equation of the line PQ is given by

y - y1 = m(x - x1)

y - 4 = -1(x + 1)

y - 4 = -x - 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