Once we are given two vertices of the triangle, since it is equilateral, we can find the length of the sides. Since the two given points are horizontally aligned their distance is the difference between their x coordinates, i.e. 10. Then, since half equilateral triangle is a 30-60-90 triangle, the height is 5sqrt(3). Then the area is easily computed as 10*5sqrt(3)/2 = 25*sqrt(3). Answer D!

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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