Class 10

Math

All topics

Coordinate Geometry

Find the coordinates of the point which divides the join of $A(−5,11)$ and $B(4,−7)$ in the ratio $7:2$.

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 $A(−5,11)$ and $B(4,−7)$ in the ratio $7:2$.

$x=(7×4+2×(−5))/(7+2)$

$=(28−10)/9$

$=18/9$

$=2$

$y=(7×(−7)+2×11)/9$

$=(−49+22)/9$

$=−27/9$

$=−3$

Therefore, required point is $(2,−3)$.