The value of m for which the points (3,5), (m,6) and (12,152) are collinear is
The points are collinear if the area of the triangle formed by these three points is zero.
Let the points be
A(3,5), B(m,6) and C(12,152)
ar△ABC=12[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]
Substituting the values
12[3(6−152)+m(152−5)+12(5−6)]=0
⇒3(−32)+5m2−12=0
⇒−92−12+5m2=0
⇒−102+5m2=0
⇒5m=10⇒m=2