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Question
Show that the following points taken in order to form an isosceles triangle
A(6, −4), B(−2, −4), C(2, 10)
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((-2 - 6)^2 + (-4 + 4)^2`
= `sqrt((-8)^2 + 0)`
= `sqrt(64)`
= 8
BC = `sqrt((2 + 2)^2 + (10 + 4)^2`
= `sqrt((4)^2 + (14)^2`
= `sqrt(16 + 196)`
= `sqrt(212)`
AC = `sqrt((2 - 6)^2 + (10 + 4)^2`
= `sqrt((- 4)^2 + (14)^2`
= `sqrt(16 + 196)`
= `sqrt(212)`
BC = AC = `sqrt(212)` ...(Two sides are equal)
∴ ABC is an isosceles triangle.
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