Find the coordinates of the point which divides the line joining (- 1, 7) and (4, – 3) in the ratio 2:3?

Here \$(x_1, y_1) = (-1, 7), (x_2, y_2)\$ = (4, -3) and \$ m:n = 2:3\$

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{2(4) + 3(-1)}{2 + 3}, \frac{2(-3) + 3(7)}{2 + 3} ) \$

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

\$\Rightarrow ( \frac{8 -3}{5}, \frac{-6 + 21}{5} ) \$

Subtract.

\$\Rightarrow ( \frac{5}{5}, \frac{15}{5} ) \$

Cancel out commmon factor.

\$\Rightarrow ( \frac{ \cancel{5} ^{1} }{ \cancel{5} ^{1}}, \frac{ \cancel{15} ^{3} }{ \cancel{5} ^{1}} )\$

Answer

The point which divides the line segment joining the points (–1, 7) and (4,–3) in the ratio 2:3 is (1, 3).