Question

Find the coordinates of the point which divides the join of points $(-1,7)$ and $(4,-3)$ in the ratio $2:3$

Answer 1

Given: $A:(x_1,y_1)=(-1,7)$

$B:(x_2,y_2)=(4,-3)$

To find: $P(x,y)suchthatAP:PB=2:3$

Solution: From section formula, coordinates of point $P$ that divides the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ are $(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Hence, coordinates of point $P$ are: $(x,y)=(\frac{2\times 4+3\times -1}{2+3},\frac{2\times -3+3\times 7}{2+3})$

$\Rightarrow (1,3)$