The coordinates 3

The coordinates of two vertices of an equilateral triangle are (1,1) and (5,1). What are the coordinates of the third vertex?

Correct answer:

x =  3
y1 =  4.4641
y2 =  -2.4641

Step-by-step explanation:

A=(1,1) B=(5,1) C=(x,y)  a=dist(A,B)=AB=(AxBx)2+(AyBy)2=(15)2+(11)2=4 a=b=c=4  Ay=By AB  Ox x=2Ax+Bx=21+5=3
a2 = (a/2)2 +h2  h=a2(a/2)2=42(4/2)2=2 33.4641  y1=Ay+h=1+3.4641=4.4641
y2=Ayh=13.4641=2.4641



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