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

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

(1, -1), (5, 2) and (9, 5)

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