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  4. The ratio in which the point P. whose abscissa is 3, divides the join of A(6,5) and B(-1,4) is equal to

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Q. The ratio in which the point $P$. whose abscissa is $3$, divides the join of $A(6,5)$ and $B(-1,4)$ is equal to______

AP EAMCETAP EAMCET 2020

Solution:

Let the point $P$ where abscissa is $3$, divides the join of points $A(6,5)$ and
$B(-1,4)$ is $\lambda: 1$, then
$3=\frac{-\lambda+6}{\lambda+1}$
$\Rightarrow 3 \lambda+3=-\lambda+6$
$\Rightarrow 4 \lambda=3$
$\Rightarrow \lambda: l=3: 4$