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Question
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Solution
Let the points (5, −2), (6, 4), and (7, −2) are representing 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)`
= `sqrt37`
BC = `sqrt((6-7)^2+(4-(-2))^2)`
= `sqrt((-1)^2+(6)^2)`
= `sqrt(1+36)`
= `sqrt37`
CA = `sqrt((5-7)^2+(-2-(-2))^2)`
= `sqrt((-2)^2+0^2)`
= `sqrt(4+0)`
= 2
Therefore, AB = BC ≠ CA
As two sides are equal in length, therefore, ABC is an isosceles triangle.
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