Question 477701: Two vertices of an equilateral triangle are (4,0) and (-6,0). find the coordinates of the point(s) that represent the 3rd vertex. Answer by Mathmama(2) (Show Source):
You can put this solution on YOUR website! First in an equilateral triangle all the sides are the same length
Let's call the triangle ABC where A(4,0) B(-6,0) and C (x,y)
the sides of the triangle are AB, BC and AC
To find the length of a side of the Triangle we need to use the formula to calculate the distance between two points (x1, y1) and (x2, y2)
Distance =
Distance AB =
=
= = 10
Since all sides are equal then length of BC = 10 and length of AC is also 10
Distance BC =
=
Distance AC =
=
BC = AC =
If we square both sides
=
Subtract from both sides
=
Expand
Subtract from both sides
Add 8x to both sides and subtract 36 from both sides
36 + 12x = 16 - 8x
-36 +8x -36 + 8x
20x = - 20
Divide both sides by 20
x = -1
So the x-coordinate is -1
Using the formula for length of BC and plugging in the x-coordinate -1
Distance BC = = 10
= 10
= 10 = 10 = 10
Square both sides = 100
Subtract 25 from both sides = 75
Take square root of both sides
y = + or y = -
y = + or y = -
The possible coordinates of the third vertex are (-1, +5) and (-1, -5)
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