SOLUTION: If in an eqilateral triangle ABC the coordinates of B and C are (1,0) and (5,0) respectivly. What are coordinates of A?

Algebra ->  Triangles -> SOLUTION: If in an eqilateral triangle ABC the coordinates of B and C are (1,0) and (5,0) respectivly. What are coordinates of A?      Log On


   

Question 499225: If in an eqilateral triangle ABC the coordinates of B and C are (1,0) and (5,0) respectivly. What are coordinates of A?
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
We would have to use the distance formula
D = sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
Now, we find the distance from B to C.
BC = sqrt%28%285+-+1%29%5E2+%2B+%280-+0%29%5E2%29
BC = sqrt%28%284%29%5E2+%29
BC = 4.
===============================================================================
Since this is and equilateral trinangle, the sides will be equal to a distance of 4.
Trying different numbers, the point for A I came up with is (3, sqrt%2812%29)
================================================================================
AB = sqrt%28%283+-+1%29%5E2+%2Bsqrt%2812%29%5E2%29
AB = sqrt%28%282%29%5E2+%2B+12+%29
AB = sqrt%2816%29
AB = 4
===============================================================================
AC = sqrt%28%283+-+5%29%5E2+%2Bsqrt%2812%29%5E2%29
AC = sqrt%28%28-2%29%5E2+%2B+12+%29
AC = sqrt%2816%29
AC = 4
==============================================================================
This does check.
The point will be (3, sqrt%2812%29)
Cleomenius