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

Answer:

T(6,5)

Step-by-step 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,

$x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Let,

(x,y)=(a,b)

(x₁,y₁)=(-4,10)

(x₂,y₂)=(10,3)

m₁:m₂=5:2

Now substitute the values.

$\hookrightarrow x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}\\\\\hookrightarrow a=\frac{5\times10+2\times(-4)}{5+2},b=\frac{5\times3+2\times10}{5+2}\\\\\hookrightarrow a=\frac{42}{7},\: b=\frac{35}{7}\\\\\hookrightarrow a=6, \:b=5$