Question

Show that three points $A(1,-2),B(3,4)andC(4,7)$ are lie an a straight line.

Answer 1

$m_1=slopeofAB=\frac{4-(-2)}{3-1}=3$
$m_2=slopeofBC=\frac{7-4}{4-3}=3$
$\therefore m_1=m_2$
$\therefore$ AB is parallel to BC and B is common to both AB and BC. Hence, the points. A
$(1,-2),B(3,4)andC(4,7)$ are collinear.
i.e., A, B, C lie on a straight line.