Question

ABC is an equilateral triangle the coordinates of vertices B and C are (3,0) and (-3,0)respectively find the coordinates of vertex A

Answer 1

hope this answer will help you to solve this problem


please mark as brainliest answer

Answer 2

$\huge\underline\mathbb{AnSwEr}$

Since ABC is an equilateral triangle, therefore

AB = AC = BC

OB = 3 units ( along + ve direction of x-axis)

OC = -3 units ( Along - ve direction of x-axis)

But side CB = OB - OC

=> CB = 3 - ( -3)

=> CB = 6 units

=> BC = 6 units

=> AC = BC = 6 units

In right traingle AOC, we have

$ac {}^{2} = ao^{2} + oc {}^{2}$

$(6) {}^{2} = oa {}^{2} + (3) {}^{2}$

$36 = oa {}^{2} + 9$

$OA {}^{2} = 36 - 9$

$OA {}^{2} = 27$

$OA = 3 \sqrt{3} \: units$

The point A is at

$3 \sqrt{3}$

and x co-ordinates of A is O

Hence,

The co-ordinates of vertex A are (0, 3✓3)