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Question
Show that the following points taken in order to form an isosceles triangle
A(5, 4), B(2, 0), C(−2, 3)
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Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((2 - 5)^2 + (0 - 4)^2`
= `sqrt((- 3)^2 + (- 4)^2`
= `sqrt(9 + 16)`
= `sqrt(25)`
= 5
BC = `sqrt((-2 - 2)^2 + (3 - 0)^2`
= `sqrt((-4)^2 + (3)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
AC = `sqrt((-2 - 5)^2 + (3 - 4)^2`
= `sqrt((-7)^2 + (-1)^2`
= `sqrt(49 + 1)`
= `sqrt(50)`
= `sqrt(25 xx 2)`
= `5sqrt(2)`
AB = BC = 5 ...(Two sides are equal)
∴ ABC is an isosceles triangle.
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