Question

2) Find the co-ordinates of point P. If P divides the line segment joining the points A (-3,7) and B (1,-4) in the ratio 2:1​

Answer 1

Given :

A point P divides the line segment joining the point A (-3,7) and B (1,-4) in the ratio 2 : 1

To find :

• Coordiantes of point P (x, y) = ?

Formulae required :

• Section formula

$\red{\bigstar}\boxed{\sf{(x\;,\;y)=\left(\dfrac{mx_2+nx_1}{m+n}\;,\;\dfrac{my_2+ny_1}{m+n}\right)}}$

[ Where (x,y) are the coordinates of point which divide the line segment joining points (x₁, y₁) and (x₂, y₂) in the ratio m : n ]

Solution :

Using section formula

$\longrightarrow\sf{(x\;,\;y)=\left(\dfrac{(2)(1)+(1)(-3)}{(2+1)}\;,\;\dfrac{(2)(-4)+(1)(7)}{(2+1)}\right)}$

$\longrightarrow\sf{(x\;,\;y)=\left(\dfrac{2-3}{3}\;,\;\dfrac{-8+7}{3}\right)}$

$\longrightarrow\red{\sf{(x\;,\;y)=\left(\dfrac{-1}{3}\;,\;\dfrac{-1}{3}\right)}}$

Therefore,

• Point P with coordinates $\bf{\bigg(\dfrac{-1}{3}\;,\;\dfrac{-1}{3}\bigg)}$ will divide the Line segment joining points A and B in the ratio 2 : 1.

Answer 2

The ratio in which P divides A(–1,7) and B(4,–3) is 2 : 3. Thus, the coordinates of point P are (1, 3).