What is the area of an equilateral triangle with vertices at (–1, –3), (9, –3), and (m, n) where m and n are both positive numbers?

A. \(25 \sqrt{2}\)

B. \(50 \sqrt{2}\)

C. \(10 \sqrt{3}\)

D. \(25 \sqrt{3}\)

E. \(50 \sqrt{3}\)
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Since it is already given that it is equilateral triangle

then all sides are equal and the distance between the sides of the co -ordinate points (–1, –3), (9, –3) is 10 (\(\sqrt{((-1-9)^2 +(-3 +3)^2}\))

Hence all sides are S = 10

since the area of equilateral triangle is \(\sqrt{3}\) /4 X side ^2

therefore putting the values we get \(\sqrt{3}\) /4 X 100 = 25\(\sqrt{3}\)
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