Question

In the given figure,ABC is an equilateral triangle. The coordinates of vertices B and C are (-3,0) and (3,0) respectively. Find the coordinates of A.

Answer 1

Answer:

(0,3√3)

Step-by-step explanation:

we need to find the height

use Pythagoras's theorem

3²+x²=6²

x=√27

x=3√3

we get the co ordinates

on y axis

so the point A(0,3√3)

Answer 2

Answer:

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}ac

2

=ao

2

+oc

2

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

2

=oa

2

+(3)

2

36 = oa {}^{2} + 936=oa

2

+9

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

2

=36−9

OA {}^{2} = 27OA

2

=27

OA = 3 \sqrt{3} \: unitsOA=3

3

units

The point A is at

3 \sqrt{3}3

3

and x co-ordinates of A is O

Hence,

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