Class 10

Math

All topics

Coordinate Geometry

For what value of y are points $P(1,4),Q(3,y)$ and $R(−3,16)$ are collinear?

Points are $P(1,4),Q(3,y)$ and $R(−3,16)$ are collinear.

Which means area of triangle PQR$=0$

Area of triangle $=21 [x_{1}(y_{2}−y_{3})+x_{2}(y_{3}−y_{1})+x_{3}(y_{1}−y_{2})]$

$=21 [1(y−16)+3(16−4)+(−3)(4−y)]$

$=21 [y−16+3×12−12+3y]$

$=21 [4y−16+36−12]=21 [4y+8]$

Since points are collinear:

$21 (4y+8)=0$

or $y=−2$.