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Using the Distance Formula, Show that the Given Points Are Collinear: (-1, -1), (2, 3) and (8, 11) - Mathematics

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

(-1, -1), (2, 3) and (8, 11)

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Solution

Let A(-1, -1) , B(2,3) and C( 8,11) be the give points. Then

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

`BC=sqrt((8-2)^2 +(11-3)^2 = sqrt(6)^2 +(8)^2 = sqrt(100) `= 10 units

`AC = sqrt(( 8+1)^2 +(11+1)^2 ) = sqrt((9)^2 +(12)^2 = sqrt(225) `= 15 units

∴ AB +BC = (5+10)  units  = 15 units   = Ac

Hence, the given points are collinear

Concept: Distance Formula
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 18.3

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