SOLUTION: Find coordinates for the point equidistant from (2,1) (2,-4) (-3,1) Please i really need your help ! thankyou

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Question 442382: Find coordinates for the point equidistant from (2,1) (2,-4) (-3,1)
Please i really need your help ! thankyou
Found 3 solutions by MathLover1, Edwin McCravy, josmiceli:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!

Find coordinates for the point equidistant from (2,1) (2,-4) (-3,1)

Let P(x, y) be the point.
The distance between (x, y) and (2, 1) is:

The distance between (x, y) and (2, -4) is:

The distance between (x, y) and (-3, 1) is:

So we have the following system of equations in terms of x, y, and D:

Square through the square roots:

Since these all equal D^2, we have two equations set equal to each other and we will produce a system of two equations that we are all used to.
Setting equation 1 = equation 2:

...now find

Setting equation 1 = equation 3:

so, the point is (-1/2, -2/5)

Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Find coordinates for the point equidistant from (2,1) (2,-4) (-3,1)

You don't need to do all that calculating the other tutor did. First we plot the points: Then we draw the triangle: That is an isosceles right triangle, so the midpoint of its hypotenuse is equidistant from the three vertices. So the midpoint is found by averaging the coordinates of the endpoints of the hypotenuse: If you like you can draw a circle with that point as the center and the three given points will be equidistance from the center: Edwin

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Call the point equidistant from the 3 given points (x,y)
The distance, , from (2,1)
(1)
The distance, , from (2,-4)
(2)
The distance, , from (-3,1)
(3)
-----------------------------
From (1) to (2)

Subtract from both sides

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From (2) to (3)

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The coordinates of the point are (-1/2,-3/2)
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check answer:
(1)
(1)
(1)
(1)
(1)
(1)
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(2)
(2)
(2)
(2)
(2)
(2)
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(3)
(3)
(3)
(3)
(3)
(3)