Question

If (3,2) (3,-2) (0,h) are the vertices of an equilateral triangle and h < 0 then h=?
Answerv with full steps

Answer 1

hai friend,

here is your answer,


let the points be

A(3,2)

B(3,-2)

C(0,h)


The distance between A and B

=√(x2-x1)²+(y2-y1)²

=√(3-3)²+(-2-2)²

=√0+16

=√(16)

=4


The distance between B and C

=√(x2-x1)²+(y2-y1)²

=√(0-3)²+(-h-2)²

=√9+h²+4+4h

=√13+h²+4h






The distance between C and A


=√(x2-x1)²+(y2-y1)²

=√(0-3)²+(h-2)²

=√9+h²+4-4h

=√13+h²-4h

as it is a equilateral triangle

AB=BC=CA


=√13+h²+4h =√13+h²-4h=4

we get

h²+4h-3=0

h²-4h-3=0


adding the equations we get


2h²-6=0

h²-3=0

h²=3

h²=√3