Let A =(x1,y1) =(5,1)
B =(x2,y2) = (-2,-3)
C = (x3,y3) = (8,2m)
Since, the points A = (5,1),B = (-2,-3) and C = (8,2m) are collinear.
∴Area of ΔABC=0⇒12[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]=0⇒12[5(−3−2m)+(−2)(2m−1)+8(1−(−3))]=0⇒12(−15−10m−4m+2+32)=0⇒12(−14m+19)=0⇒m=1914Hence, the required value of m is 1914.