Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear
Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear
Solution and Explanation
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)
\(\therefore\) 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=\(\sqrt{(1-(-2))^2+(5-(-11))^2}=\sqrt{3^2+16^2}=\sqrt{9+256}=\sqrt{265}\)
Since, AB+BC\(\neq\)CA
Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.
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Concepts Used:
Coordinate Geometry
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.