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Question

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___


A

B=(2,23)
C =(4,0)

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B

C=(2,2)
B =(4,0)

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C

C=(2,23)
B =(4,0)

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D

B=(2,2)
C =(4,0)

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Solution

The correct option is C

C=(2,23)
B =(4,0)


In equilateral triangle ABC draw CD to AB, then D will be the mid-point of AB.

B is on X-axis and AB =4 B=(4,0)

Given AB =4

AD=12×AB

=2 units.

x coordinate of C is 4.

Now ADC makes right angled triangle with ADC=90

AC2=AD2+DC2

42=22+DC2

DC2=164

=12

DC=23

Coordinates of C=(2,23)

Remaining vertices are B(4,0) and C=(2,23)


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