Class 10

Math

All topics

Coordinate Geometry

Point A lies on the line segment PQ joining $P(6,−6)$ and $Q(−4,−1)$ in such a way that $PA/PQ=2/5$. If the point A also lies on the line $3x+k(y+1)=0$, find the value of k.

Let the point $A(x,y)$ which lies on line joining $P(6,−6)$ and $Q(−4,−1)$ such that $PA/PQ=2/5$

Line segment PQ is divided by the point A in the ratio $2:3$.

Step $1$: Find coordinates of $A(x,y)$

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

$x=(2(−4)+3(6))/(2+3)$

$=(−8+18)/5$

$=10/5=2$

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

$y=(2(−1)+3(−6))/5$

$=(−2−18)/5$

$=−20/5$

$=−4$

Step $2$: Point A also lies on the line $3x+k(y+1)=0$

$3(2)+k(−4+1)=0$

$6−3k=0$

or $k=2$.