Find the points which divides the line segment joining (–3, –4) and (–8, 7) internally in the ratio 7:5.

Here \$ (x_1, y_1) = (–3, –4), (x_2, y_2) = (-8, 7) \$ and\$ m:n = 7:5 \$.

The required point is given by

\begin{align} \Bigl( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \Bigr) \end{align}

Substitute the values.

\$\Rightarrow (\frac{7(-8) + 5(-3)}{7 + 5}, \frac{7(7) + 5(-4)}{7 + 5} ) \$

Multiply in the numerator and sum the values in the denominator.

\$\Rightarrow ( \frac{-56 - 15}{12}, \frac{49 - 20}{12})\$

Add and subtract.

\$\Rightarrow ( \frac{-71}{12}, \frac{29}{12} )\$

Answer

The point which divides the line segment joining the points (–3, –4) and (-8, 7) internally in the ratio 7:5 is \$ ( \frac{-71}{12}, \frac{29}{12} ) \$.