math geniuses!! pls help me!!!!?

Question

m(1,-5) is the midpoint of RS(with a line over the RS). If S has coordinates (5,1), find the coordinates of R.

please explain how to do this!!!!

Answer 1

to find the midpoint it is ((x1+x2)/2, (y1+y2)/2)
so (5+x2)/2=1 and (1+y2)/2 = -5
x2 = 2-5 = -3
y2 = -10-1 = -11

Answer 2

Okay, first recognise that this problem is about a line that starts at point R, and goes to point S.

You are told the midpoint and the end point and you need to find the start point.

If you were to plot the two points given (the midpoint 1,-5 and the S point 5,1) you would be able to graphically find the start point and see exactly how it fits together. Not easy to do on Yahoo answers but you should try it.

You could use the midpoint formular (I'll do it that way next) or you could just use a little logic like this:

the midpoint has x=1, and y=-5. To go from mid to end you have to get to x=5, and y=1. That means going positive 4 in the x direction and +6 in the y direction. If you want to start at the middle and go to the beginning you go just the opposite. That is, negative 4 in the x direction and positive -6 in the y, and that gets you to x=-3, and y=-11 so (-3,-11) is the point R.

The midpoint formula gives you the midpoint of a line if you know its ends. It can also be used to give you either end if you know the midpoint and the other end point. It is actually just averaging the x and y values so that you get the average or middle value.

Xm=(Xr+Xs)/2
Ym=(Yr+Ys)/2

If you substitute the known values from the problem you get:

1=(Xr+5)/2
2=Xr+5
-3=Xr

-5=(Yr+1)/2
-10=Yr+1
-11=Yr

so the point R checks as (-3,-11)

If that isn't clear, then you should plot the points on an x-y graph and I think you will see exactly how it works.

good luck

Answer 3

find the slope of the line segment using the points you have. since slope is rise/run, use the slope to move the point from the midpoint to the endpoint you need. if the endpoint you have is 4 below and 3 to the right of the midpoint, the other endpoint will be 4 above and 3 to the left of the midpoint (opposite to whatever the original point is). if you were to fold the paper over so that the endpoints were touching, the line segment would be perpendicular to the crease in the paper. use the distance from the midpoint to the given endpoint and again from the midpoint to the newly found endpoint to make sure they are the same distance form the midpoint, otherwise you've made a mistake

Answer 4

Genius is not required - just graph it. Using graph paper make your point S at (5,1), then make your midpoint m at (1,-5). Note you have to count left 4 and down 6 to get to the midpoint. So, count left 4 more and down 6 more to get to R.

Answer 5

well it goes RmS the distance from s to m is 4,-4 (over 4, 6 down) so take that from the midpoint to get R=(-3,11)