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Chapter 11: Q. 58 (page 741)

Geometry: Collinear Points Using the result obtained in Problem 57, show that three distinct points x1,y1,x2,y2,andx3,y3are collinear (lie on the same line) if and only if

x1y11x2y21x3y31=0

Short Answer

Expert verified

It is proved that the given pointsx1,y1,x2,y2,andx3,y3 are collinear only if,

x1y11x2y21x3y31=0

Step by step solution

01

Step 1. Given Information  

We are given three x1,y1,x2,y2,andx3,y3 points.

We have to show that the above points are collinear only if,

x1y11x2y21x3y31=0

02

Step 2. Proving the collinear points

The equation of a line passing through two points x1,y1,x2,y2is given by,

xy1x1y11x2y21=0

Since, all points lie on the same line, so

x3y31x1y11x2y21=0

or

x1y11x2y21x3y31=0

Hence Proved.

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