Question

if two vertices of Equalitral trias triangle are o,o) and(3root3) find the codinate of kind vertres​

Answer 1

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Let us assume C(x, y) be the third vertex of the triangle. We have AB = BC = CA

We know that the distance between the two points (x1, y1) and (x2, y2) is √(x1 - x2) ² + (y1 - y2) ²

Now, ⇒ BC = CA ⇒ BC2 = CA2 ⇒ (3 - x)2 + (√3 - y)2 = (x - 0)2 + (y - 0)2 ⇒ x2 - 6x + 9 + 3 + y2 - 2√3y = x2 + y2 ⇒ 6x = 12 - 2√3y ⇒ AB = BC ⇒ AB2 = BC2 ⇒ (0 - 3)2 + (0 - √3)2 = (3 - x)2 + (√3 - y)2 ⇒ 9 + 3 = 9 - 6x + x2 + 3 - 2√3y + y2 From (1) ⇒ 48y2 - 48√3y - 288 = 0 ⇒ y2–√3y –6 = 0 ⇒ y2 - 2√3y + √3y - 6 = 0 ⇒ y(y - 2√3) + √3(y - 2√3) = 0 ⇒ (y + √3)(y - 2√3) = 0 ⇒ y + √3 = 0 (or) y - 2√3 = 0 ⇒ y = - √3 (or) y = 2√3 From (1), for y = √3

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