Question

A point T divides a line AB internally in the ratio5:2 .Given that A is (-4,10) and B is (10,3) , find the coordinates of T

Answer 1

T(6,5)

Explanation:

Solution,

Let the coordinate of T be T(a,b), where T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3).

From the section formula,

`x=(m_1x_2+m_2x_1)/(m_1+m_2),y=(m_1y_2+m_2y_1)/(m_1+m_2)`

Let,

(x,y)=(a,b)

(x₁,y₁)=(-4,10)

(x₂,y₂)=(10,3)

m₁:m₂=5:2

Now substitute the values.

`\hookrightarrow x=(m_1x_2+m_2x_1)/(m_1+m_2),y=(m_1y_2+m_2y_1)/(m_1+m_2)\\\\\hookrightarrow a=(5*10+2*(-4))/(5+2),b=(5*3+2*10)/(5+2)\\\\\hookrightarrow a=(42)/(7),\: b=(35)/(7)\\\\\hookrightarrow a=6, \:b=5`