Question
Find the coordinates of the point which divides the line segment joining $(-1, 3)$ and $(4, -7)$ internally in the ratio $3 : 4.$
✓
Answer
Let P(x, y) be the required point.
$\text{x}=\frac{\text{mx}_2+\text{nx}_1}{\text{m}+\text{n}}$
$\text{y}=\frac{\text{my}_2+\text{ny}_1}{\text{m}+\text{n}}$
Here, $x_1 = -1$
$y_1 = 3$
$x_2= 4$
$y_2= -7$
$m : n = 3 : 4$
$\text{x}=\frac{3\times4+4\times(-1)}{3+4}$
$\text{x}=\frac{12-4}{7}$
$\text{x}=\frac{8}{7}$
$\text{y}=\frac{3\times(-7)+4\times3}{3+4}$
$\text{y}=\frac{-21+12}{7}$
$\text{y}=\frac{-9}{7}$
$\therefore$ The coordinates of P are $\Big(\frac{8}{7},\frac{-9}{7}\Big).$
$\text{x}=\frac{\text{mx}_2+\text{nx}_1}{\text{m}+\text{n}}$
$\text{y}=\frac{\text{my}_2+\text{ny}_1}{\text{m}+\text{n}}$
Here, $x_1 = -1$
$y_1 = 3$
$x_2= 4$
$y_2= -7$
$m : n = 3 : 4$
$\text{x}=\frac{3\times4+4\times(-1)}{3+4}$
$\text{x}=\frac{12-4}{7}$
$\text{x}=\frac{8}{7}$
$\text{y}=\frac{3\times(-7)+4\times3}{3+4}$
$\text{y}=\frac{-21+12}{7}$
$\text{y}=\frac{-9}{7}$
$\therefore$ The coordinates of P are $\Big(\frac{8}{7},\frac{-9}{7}\Big).$
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