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Question

If two vertices of an equilateral triangle are (0,0),(3,3), find the third vertices of the triangle.

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Solution

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)=(32+3)=(x3)2+(y3)2

x2+y2=12

x2+96x+y2+323y=12

246x23y=12

6x23y=12

3x+3y=6

x=63y3

(63y)32+y2=12

(36+3y2123y)9+y2=12

36+3y2123y+9y2=108

123y+12y272=0

3y+y26=0

(y23)(y+3)=0

y=23or3

Ify=23,x=(66)/3=0

Ify=3,x=93=3

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


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