Question

find the co_ ordinates of the point, which divides the line joining A(0, 0) and B(5, 10 ) in the ratio of 2:3​

Answer 1

Answer:

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From question,

m:n = 2:3

Given points,

A(0, 0) and B(5 , 10)

From points :

• ${ \sf{ x_{1} = 0}}$
• $\: { \sf{ x_{2} = 5}}$
• $\: { \sf{ y_{1} = 0 }}$
• $\: { \sf{ y_{2} = 10 }}$

Let's find the coordinate points:

By using formula,

${ \sf \bigg({ \frac{m x_{2} + n x_{1}}{m + n} , \frac{my_{2} + n y_{1} }{m + n} \bigg) }}$

By Substituting Values,

${ \implies{ \sf{ \bigg( \frac{2(5) + 3(0)}{2 + 3}, \frac{2(10) + 3(0)}{2 + 3} \bigg) }}}$

${ \implies{ \sf{ \bigg( \frac{10 + 0}{5}, \frac{20 + 0}{5} \bigg) }}}$

${ \implies{ \sf{ \bigg( \frac{10}{5}, \frac{20}{5} \bigg) }}}$

${ \implies{ \sf{ \big(2,4 \big) = \big(x,y \big)}}}$

Therefore,

• p(x, y) = (2, 4)