Let , and be three distinct points with…

MATHEMATICS · Multi-part · CBSE · Mathematics · Straight Lines · Straight Lines

Problem

Let

P(x_1,y_1)

Q(x_2,y_2)

and

R(x_3,y_3)

be three distinct points with

x_1\neq x_2\neq x_3

. (a) Prove that if the slopes of

PQ

and

QR

are equal, then

P

Q

and

R

are collinear. (b) Explain why the converse is also true for non-vertical points, and state what additional consideration is needed when any two of the points have the same

x

-coordinate.

Related theory

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

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