Question

Find the value of m, if the points (5,1) (-2,-3) and (8,2m) are collinear.

Answer 1

Let A =$(x_1,y_1)$ =(5,1)
B =$(x_2,y_2)$ = (-2,-3)
C = $(x_3,y_3)$ = (8,2m)
Since, the points A = (5,1),B = (-2,-3) and C = (8,2m) are collinear.
$\therefore Areaof\Delta ABC=0\Rightarrow \frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0\Rightarrow \frac{1}{2}\left[5\right(-3-2m)+(-2\left)\right(2m-1)+8(1-(-3)\left)\right]=0\Rightarrow \frac{1}{2}(-15-10m-4m+2+32)=0\Rightarrow \frac{1}{2}(-14m+19)=0\Rightarrow m=\frac{19}{14}\text{Hence, the required value of m is}\frac{19}{14}$.