If A(1,2), B(4,5) and C(7,8) are three distinct points in the coordinate plane

MATHEMATICS · Single correct · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

If A(1,2), B(4,5) and C(7,8) are three distinct points in the coordinate plane, which one of the following conditions is sufficient to ensure that A, B and C are collinear? (a)

m_{AB}\,\times\,m_{BC}=-1

(b)

|m_{AB}|=|m_{BC}|

(c)

m_{AB}=m_{BC}

(d)

m_{AB}=-\,m_{BC}

Related theory

Straight Lines
Coordinate Geometry
Slope and angle between lines
Slope using coordinates

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