Question

The quadrant in which the point dividing the line segment joining the points (7, –6) and (3, 4) internally in the ratio 1 : 2 is ______.

Answer 1

The quadrant in which the point dividing the line segment joining the points (7, –6) and (3, 4) internally in the ratio 1 : 2 is IV.

Explanation:

Let A(7, –6) and B(3, 4). 

If P divides AB internally in the ratio 1 : 2, then by the section formula

`x = (1 xx 3 + 2 xx 7)/(1 + 2) = 17/3` (positive)

`y = (1 xx 4 + 2 xx (-6))/(1 + 2) = -8/3` (negative)

Since x > 0 and y < 0, P lies in the fourth quadrant.