Question

The coordinates of a point dividing the line segment joining (1, 2) and (4, 5) internally in the ratio 2:1 is ____________________

(a) (3, 4)

(b) (4, 3)

(c) (5, 4)

(d) (5, 3)

The question was posed to me in final exam.

This question is from Slope of a Line topic in section Straight Lines of Mathematics – Class 11

Answer 1

The correct option is (a) (3, 4)

Explanation: The coordinates of a point dividing the line segment joining (x1, y1) internally in the ratio m: n is \((\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})\).

So, the coordinates of a point dividing the line segment joining (1, 2) and (4, 5) internally in the ratio 2:1 is \((\frac{2*4+1*1}{2+1}, \frac{2*5+1*2}{2+1})\) = (3, 4).