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Which condition was used to conclude that the points $A(3,1)$, $B(6,4)$ and $C(8,6)$ in Fig. 7.6 are collinear? 
A$AB=BC$
B$AB^2+BC^2=AC^2$
C$AB+BC=AC$
DTheir $x$-coordinates are consecutive
Answer & Solution
Correct answer: C. $AB+BC=AC$
For the given points, $AB=3\sqrt{2}$, $BC=2\sqrt{2}$ and $AC=5\sqrt{2}$. Since $AB+BC=AC$, point B lies on the segment joining A and C, so the three points are collinear. Option B would indicate a right triangle, not necessarily collinearity.
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