Class 10

Math

All topics

Coordinate Geometry

Find the coordinates of the point which divides the join of $A(−1,7)$ and $B(4,−3)$ in the ratio $2:3$.

If a point $P(x,y)$ divides a line segment having end points coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$, then coordinates of the point P can be find using formula:

$x=m_{1}+m_{2}m_{1}x_{2}+m_{2}x_{1} $

$y=m_{1}+m_{2}m_{1}y_{2}+m_{2}y_{1} $

Let $P(x,y)$ be the point which divides the line joining the points $A(−1,7)$ and $B(4,−3)$ in the ratio $2:3$, then

$x=(2×4+3×(−1))/(2+3)$

$=(8−3)/5$

$=5/5$

$=1$

$x=1$.

$y=(2×−3+3×7)/5$

$=(−6+21)/5$

$=15/5$

$=3$

$y=1$

Therefore, required point is $(1,3)$.