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Question

IF the two vertices of an equilateral triangle be (0,0) and (3,3 ) , then the co-ordinates of third vertex are

A
(0,23) or (3,3)
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B
(0,3) or (3,3)
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C
(0,2) (0,3)
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D
none of these
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Solution

The correct option is B (0,23) or (3,3)

Given that, Two vertices of an equilateral triangle are (0,0) and (3,3)

Let the third vertex of the equilateral triangle be (x,y)

Distance between (0,0) and(x,y) =Distance between(0,0) and(3,3) =Distance between(x,y)and (3,3).

x2+y2=(x3)2+(y3)2

x2+y2=(x3)2+(y3)2

x2+y2=12

x2+96x+y2+323y=12

246x23y=12

6x23y=12

6x+23y=12

3x+3y=6

x=(63)3

[63y3]3+y2=12

(36+3y2123y)9+y2=12

36+3y2123y+9y2=108

123y+12y272=0

(y23)(y+3)=0

y=23or3

ify=23,x=(66)3=0

ify=3,x=(6+3)3=3

So, the third vertex of the equilateral triangle =(0,23) or (3,3).


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