Question

An equilateral triangle has two vertices at the points (3,4) and (-2,3).Find the coordinates of third vertex.

Answer 1

Use the distance formula to get the coordinates of 3rd side

Answer 2

HEY DEAR ... ✌️

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Here's , ur answer :-

Let 3rd vertex of an equilatral triangle is (x, y)
we know,
all side of equilatral triangle are same
so,
(x-3)^2+(y-4)^2=(x+2)^2+(y-3)^2=(5)^2+(1)^2

now,
(x-3)^2+(y-4)^2=(x+2)^2+(y-3)^2
-6x-8y+9+16=4x-6y+4+9
10x+2y=12
5x+y=6 -----------------(1)

again ,
(x+2)^2+(y-3)^2=25+1
x^2+y^2+4x-6y=13--------------(2)
solve equation (1) and (2)
x= {1+root3}/2 and {1-root3 }/2
and y=6-5x

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HOPE , IT HELPS ... ✌️