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Using the Distance Formula, Show that the Given Points Are Collinear: (1, -1), (5, 2) and (9, 5) - Mathematics

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Using the distance formula, show that the given points are collinear:  

 (1, -1), (5, 2) and (9, 5)

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Solution

Let A (1,-1), B(5,2)  and C(9,5) be the give points. Then

`AB= sqrt((5-1)^2 +(2+1)^2 ) = sqrt(4^2+3^2) = sqrt(25) = 5` unts

`BC = sqrt((9-5)^2 +(5-2)^2 ) = sqrt((4^2+3^2)) = sqrt(25)` = 5 units

`AC= sqrt((9-1)^2 +(5+1)^2) = sqrt(8^2+6^2) = sqrt(100)`=10 unit

∴ AB+BC = (5+5) units = 10 units = AC 

Concept: Distance Formula
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 18.1

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