# Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear. - Mathematics

Sum

Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.

#### Solution

Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C of the given triangle respectively.

Let A = (1,5), B = (2,3), C = (-2, -11)

:.AB = sqrt((1-2)^2+(5-3)^2) = sqrt5

BC = sqrt((2-(-2))^2 + (3-(-11))^2) = sqrt(4^2+14^2) = sqrt(16+196) = sqrt(212)

CA = sqrt((1-(-2))^2 + (5-(-11))^2) = sqrt(3^2+16) = sqrt(9+256) = sqrt(265)

Since AB+BC ≠ CA

Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.

Concept: Distance Formula
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 7 Coordinate Geometry
Exercise 7.1 | Q 3 | Page 161

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