Question

How do I go about doing this problem? "Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P).
P = (10, 6) and M = (-4, 8)"

Answer 1

Let's call this other unknown point Q

Every point in general is of the form (x,y) so Q = (x,y)

Answer 2

P is one endpoint given to be P = (10,6)
Q is the other endpoint and we defined it to be Q = (x,y)

Answer 3

What we do with these two points is add up the corresponding coordinates and divide by 2 to get the midpoint coordinates

So for the x coordinates

Add up the x coordinates: 10+x

Then divide that by 2: (10+x)/2

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The midpoint is M = (-4, 8) where the x coord of the midpoint is -4

So (10+x)/2 = -4

making sense so far?

Answer 4

idk if this will help you but hear
http://openstudy.com/study#/updates/4fe8d741e4b0bbec5cf949f9

Answer 5

so the answer would be (-18,10)?

Answer 6

correct

Answer 7

Thank you very much, I'm just really bad at remembering the formulas to use, so what formula is it exactly because if i know the formula i'll be golden.

Answer 8

can i have a medal if i helped

Answer 9

this is the midpoint formula

http://www.statisticslectures.com/images/midpoint1.gif

Answer 10

I use that for finding the "other point" as well?

Answer 11

sorta, but in reverse. You don't use the formula directly

let's say the midpoint was (Xm, Ym). The m denotes midpoint

so that would mean

\[\Large (X_{m}, Y_{m}) = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) \]

that breaks up into these 2 equations
\[\Large X_{m}=\frac{x_1+x_2}{2}, \ \ Y_m = \frac{y_1+y_2}{2} \]
If you know the midpoint then (Xm, Ym) are known. You'll use those values to solve for either (x1,y1) or (x2,y2) depending on how you label your points