Subjects

Mathematics Science Social Science Civics Social Science Economics Social Science Geography Social Science History

Chapter 7 · Question 6

Find the point dividing $(1,2)$ and $(7,8)$ internally in the ratio $2:1$ .

Back to Chapter

Answer

Direct Answer

Using section formula,

x=\frac{2(7)+1(1)}{3}=5

,

y=\frac{2(8)+1(2)}{3}=6

. The point is

(5,6)

.

Simple Explanation

Cross multiply with the ratio. The point is

(5,6)

.

Exam-Ready Structure

Let

A(1,2)

and

B(7,8)

, and ratio

AP:PB=2:1

. Then

P=\left(\frac{2\cdot7+1\cdot1}{2+1},\frac{2\cdot8+1\cdot2}{2+1}\right)=\left(\frac{15}{3},\frac{18}{3}\right)=(5,6)

.

Key Points

Using section formula, $x=\frac{2(7)+1(1)}{3}=5$ , $y=\frac{2(8)+1(2)}{3}=6$ .

Related Questions

State the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ .

Find the distance between $(2,3)$ and $(6,6)$ .

Report a mistake