Question

4. In the adjoining figure, ABC is an equilateral triangle. The
coordinates of vertices B and Care (3,0) and (-3,0) respectively.
Find the coordinates of its vertex A.​

Answer 1

Answer:

Given coordinates of B and C are (3, 0) and (-3, 0)

and CD = DB = 3 units

Hence D coincides with the origin.

Since ABC is an equilateral triangle, AB = BC = CA = 6 units

In right triangle ADB, [By Pythagoras theorem]

units

Hence the coordinates of A are

Answer 2

Step-by-step explanation:

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)