Question

Find the ratio in which the line segment joining (—2, —3) and (5, 6) is divided by

(i) x-axis

(ii) y-axis.

Also, find the coordinates of the point of division in each case.

Answer 1

(i) Suppose x - axis  divides AB in the ratio K:1 at point P

Then, the coordinates of the point of division of division are

Since, P lies on x-axis, and y-coordinates of every point on x-axis is zero.

Hence, the required ratio is 1: 2

Putting K=1/2 in the coordinates of P

We find that its coordinates are (1/3,0).

(ii) Suppose y-axis divides AB in the ratio k:1 at point .Q

Then, the coordinates of the point of division are

Since, Q lies on y - axis and x-coordinates of every point on y-axis is zero.

Hence, the required ratio is 2/5:1 = 2:5

Putting k=2/5 in thee coordinates of Q.

We find that the coordinates are (0,-3/7)