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Please solve for a point on the x-axis that is equidistant from (10,4) and (6,2).
Thanks
Call point on x-axis P. It will have coordinates (x,0). We need distance from P to (6,2) to equal distance from P to (10,4).
Formula for distance between to points (a,b),(c,d) is:
So we require:
So square bot sides and expand giving:
Cancel square of x from both sides and rearrange giving:
therefore
Therefore P is the point:
Last edited by gnitsuk (2006-10-04 03:27:37)
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Picture two triangles on the graph. The first triangle will have corner points of (6,2), (6,0) and (z,0). The second will have (10,4), (10,0), and (z,0). These are right triangles. You want to find z so the the hypotenuses (h) of these 2 triangles are equal. Use the Pythagorean theorem.
For the first triangle:
Set those two equations to be equal to each other and you have:
So the point is (9.5, 0)
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Sorry about the duplicate answer. At least we came up with the same answer!
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We need a point, call it P, which is on the x-axis, and therefore of the form P = (x, 0)
The distance formula between two points is:
We need the distance between (10, 4) and P to be the same as the distance between (6, 2) and P.
Ie, we need:
to be equal to:
Setting these to be equal:
Square both sides:
Expanding:
Re-arranging:
So the point we need is:
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Haha sorry it's already done ! oops
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thanks...i was never good in math..
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