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Question

Mathematics Question on Coordinate Geometry

Check whether (5, - 2), (6, 4) and (7, - 2) are the vertices of an isosceles triangle.

Answer

Let the points (5, −2), (6, 4), and (7, −2) represent the vertices A, B, and C of the given triangle respectively.
AB=(5−6)2+(−2−4)2=(−1)2+(−6)2=1+36=37\sqrt{(5-6)^2+(-2-4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1+36}=\sqrt{37}
BC=(6−7)2+(4−(−2))2=(−1)2+(6)2=1+36=37\sqrt{(6-7)^2+(4-(-2))^2}=\sqrt{(-1)^2+(6)^2}=\sqrt{1+36}=\sqrt{37}
CA=(5−7)2+(−2−(−2))2=(−2)2+0=2\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.