## end point: find end point given midpoint, other endpoint

Geometric formulae, word problems, theorems and proofs, etc.
foxr1der31
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Joined: Tue Jul 07, 2009 2:40 am
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### end point: find end point given midpoint, other endpoint

Find the coordinates of the other endpoint when you are given the midpoint and one of the endpoints.

endpoint1 = (3,5) and midpoint = (-2,0) help and tell me how to do it

here is the formula but i dont know what do make of it maybe u guys can

x = (x2 + x1)

-2 = (1 + x1) (Distributive Property)

x1= - (subtract from both sides)

x1= -5 (multiply both sides by 2)

We now know that the x-coordinate of the missing endpoint is -5.

We will now solve for the missing y-coordinate in the same manner.

y = (y2 + y1)

4 = (2 + y1)

4 = 1 + y1 (Distributive Property)

y1 = 3 (Subtract 1 from both sides)

y1 = 6 (Multiply both sides by 2)

We have now found the coordinates of the missing endpoint:

(-5,6)

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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You can check your solution by plugging it and the original point into the Midpoint Formula and making sure you end up with the correct midpoint value:

. . . . .$\left(\frac{3\, +\, (-5)}{2},\, \frac{5\, +\, 6}{2}\right)\, =\, \left(\frac{-2}{2},\, \frac{11}{2}\right)\, =\, \left(-1,\, \frac{11}{2}\right)$

Since this does not match the given midpoint, then your solution is unlikely to be correct.

Let's try working directly from the Formula:

. . . . .$(-2,\, 0)\, =\, \left(\frac{x\, -\, 3}{2},\, \frac{y\, -\, 5}{2}\right)$

Multiplying through by 2, we get:

. . . . .$(-4,\, 0)\, =\, (x\, -\, 3,\, y\, -\, 5)$

Then x - 3 = -4 and y - 5 = 0. Where does this lead...?

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