8
Two vertices of an equilateral triangle are given
(3,4) & (-2, 3) find the & third vertex .
Answers
Answered by
1
Step-by-step explanation:
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)
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