In what ratio does the point P $(-4,6)$ divide the line segment joining the points A$(-6,10)$ and B$(3,8)$ ?

Given :

P$(-4,6)$ divides the line segment joining the points A$(-6,10)$ and B$(3,8)$.

To find :

We have to find the ratio of division.

Solution :

Let P divides AB in the ratio m:n internally. 

The section formula is,

$$(x, y) = \frac{m x_{2} + n x_{1}}{m + n} , \frac{m y_{2} + n y_{1}}{m + n} $$

$P(x, y) = P(-4,6)$ ; $A (x_{1}, y_{1}) = A(-6,10)$ ; $B(x_{2}, y_{2}) =  B(3,8)$

$(-4, 6) = \frac{m (3) + (-6)}{m + n} , \frac{m (8) + n (10)}{m + n} $

On comparing,

$-4 = \frac{3m-6n}{m + n}$

$-4(m + n) = 3m-6n$

$-4m-4n = 3m-6n$

$4m+3m+4n-6n = 0$

$7m-2n = 0$

$7m = 2n$

$\frac{m}{n} = \frac{2}{7}$

$m : n = 2 : 7$

The required ratio is 2:7.

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Updated on: 10-Oct-2022

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