In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?


In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?


Let the required ratio be $k: 1$.

Then, by section formula, the coordinates of C are

$C\left(\frac{7 k+2}{k+1}, \frac{8 k+3}{k+1}\right)$


$\frac{7 k+2}{k+1}=4$ and $\frac{8 k+3}{k+1}=5 \quad[\because C(4,5)$ is given $]$

$\Rightarrow 7 k+2=4 k+4$ and $8 k+3=5 k+5 \Rightarrow 3 k=2$ and $3 k=2$

$\Rightarrow k=\frac{2}{3}$ in each case

So, the required ratio is $\frac{2}{3}: 1$, which is same as $2: 3$.

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