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

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

The required point is given by

\$( \frac{mx_2 - nx_1}{m - n}, \frac{my_2 - ny_1}{m - n} ) \$

Substiutute the values.

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

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

\$\Rightarrow ( \frac{-56}{2}, \frac{49 + 20}{2} )\$

Cancel out commmon factor.

\$\Rightarrow ( \frac{-41}{2}, \frac{69}{2} )\$

Answer

The point which divides the line segment joining the points (-3, 4) and (-8,7) internally in the ratio 7:5 is \$ ( \frac{-41}{2}, \frac{69}{2} ) \$.