Question

an equilateral triangle has two vertices at the points (3,4)and(-2,3),find the coordinates of third vertex​

Answer 1

Answer:

all side of the equilateral triangle is the same, so,

(x−3)

2

+(y−4)

2

=

(x+2)

2

+(y−3)

2

=

(5)

2

+(1)

2

(x−3)

2

+(y−4)

2

=(x+2)

2

+(y−3)

2

=26

x

2

+y

2

−6x−8y=1

x

2

+y

2

=6x+8y+1 -------------(1)

------------------------------------

26=x

2

+y

2

+4x−6y+11

x

2

+y

2

+4x−6y=15

x

2

+y

2

=−4x+6y+15----------(2)

-----------------------------------

x

2

+9−6x+y

2

+16−8y=x

2

+y

2

+4x−6y+11

10x+3y=12 ----------------(3)

-----------------------------------

In equation (1) & (2) RHS is equal , therefore ;

6x+8y+1=−4x+6y+15

10x+2y=14--------------(4)

__________________

Solving equation (3) & (4)

y=−2

x=18

==============================

Hence the third vertex of the triangle is (−2,18)