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# Find whether the point $A(1,2),B(3,6)$&$C(5,10)$ are collinear or not?

$\begin{array}{1 1}(a)\;\text{A and B are collinear}\\(b)\;\text{B and C are collinear}\\(c)\;\text{A,B and C are collinear}\\(d)\;\text{None of these}\end{array}$

For the points to be collinear we have slope of AB =slope of BC=slope of CA
Hence slope of AB=$\large\frac{6-2}{3-1}$$=2 Slope of BC=\large\frac{4}{2}$$=2$
Slope of AC=$\large\frac{10-2}{5-1}$$=2$
Hence these three points are collinear.
Hence (c) is the correct answer.