In what ratio does the point P(– 4, y) divides the line segment joining the points A(– 6, 10) and B(3,

#Maths
#School
#Coordinate Geometry
#CBSE 10 Class

In what ratio does the point P(– 4, y) divides the line segment joining the points A(– 6, 10) and B(3, – 8)? Hence find the value of y.

Answers (1)

Given $A= \left ( x_{1} ,y_{1}\right )= \left ( -0,10 \right );B= \left ( x_{2} ,y_{2}\right )= \left ( 3,-8 \right )$
$P= \left ( x,y \right )= \left ( -4,y \right )$
To find $\rightarrow$ y coordinate of p
Let AP : PB = K:1
Section formula
$P \left ( x,y \right )= \left ( \frac{x_{1}+kx_{2}}{k+1},\frac{y_{1}+ky_{2}}{k+1} \right )$
$x= \frac{x_{1}+kx_{2}}{k+1}$
$-4= \frac{-6+kx_{3}}{k+1}$
$-4\left ( k+1 \right )= -6+3k$
$-4k-4= -6+3k$
$6-4= 4k+3k$
$\Rightarrow k= \frac{2}{7}$
use this value to calculate y coordinates of p
$y= \frac{y_{1}+ky_{2}}{k+1}$
$y= \frac{10+\frac{2}{7}\times \left ( -8 \right )}{\frac{2}{7}+1}$
$y= \frac{10-\frac{16}{7}}{\frac{3}{7}}$
$y= \frac{70-16}{3}= \frac{54}{3}= 6$
$\Rightarrow$ y coordinate of p = 6