Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution and Explanation
Let the points (5, −2), (6, 4), and (7, −2) represent the vertices A, B, and C of the given triangle respectively.
AB=\(\sqrt{(5-6)^2+(-2-4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1+36}=\sqrt{37}\)
BC=\(\sqrt{(6-7)^2+(4-(-2))^2}=\sqrt{(-1)^2+(6)^2}=\sqrt{1+36}=\sqrt{37}\)
CA=\(\sqrt{(5-7)^2+(-2-(-2))^2}=\sqrt{(-2)^2+0}=2\)
Therefore, AB=BC
As two sides are equal in length, therefore, ABC is an isosceles triangle.
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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.