SOLUTION: Please help me to solve this problem. __ M (2,4 ) is the midpoint of RS. If S has coordinates (5,0 ) find the distance from R to S.

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Question 125070: Please help me to solve this problem.
__
M (2,4 ) is the midpoint of RS. If S has coordinates (5,0 ) find the distance from R to S.
Found 2 solutions by checkley71, josmiceli:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE DISTANCE BETWEEN X=5 & X=2 IS 5-2=3.
SO THE DISTANCE BETWEEN M & R IS ALSO 3 OR 2-3=-1 THE X COORDINATE FOR THE R POINT.
THE DISTANCE BETWEEN Y=0 & Y=4 IS 4-0=4.
SO THE DISTANCE BETWEEN M & R IS ALSO 4 0R 4+4=8 THE Y COORDINATE FOR THE R POINT.
THUS WE HAVE R=(-1,8)
THE DISTANCE BETWEEN (-1,8) & (5,0) IS
5+1=6 FOR THE X AXIS.
8-0=8 FOR THE Y AXIS.
SO WE HAVE A RIGHT TRIANGLE WITH SIDES EQUAL TO 6 & 8.
NOW WE FIND THE HYPOTENUSE (DISTANCE BETWEEN R&S).
6*2+8*2=RS^2
36+64=RS^2
100=RS^2
RS=SQRT100
RS=10 ANSWER FOR THE DISTANCE BETWEEN R & S.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
M = (2,4)
S = (5,0)
The general formulas for the midpoint are
x%5Bm%5D+=+%28x%5B1%5D+%2B+x%5B2%5D%29+%2F+2
2+=+%285+%2B+x%5B2%5D%29+%2F+2
5+%2B+x%5B2%5D+=+4
x%5B2%5D+=+-1
and
y%5Bm%5D+=+%28y%5B1%5D+%2B+y%5B2%5D%29+%2F+2
4+=+%280+%2B+y%5B2%5D%29+%2F+2
y%5B2%5D+=+8
S(x,y) = (-1,8)
The distance formula is
d+=+sqrt%28%28x%5B2%5D+-+x%5B1%5D%29%5E2+%2B+%28y%5B2%5D+-+y%5B1%5D%29%5E2%29
d+=+sqrt%28%28-1+-+5%29%5E2+%2B+%288+-+0%29%5E2%29
d++=+sqrt%2836+%2B+64%29
d+=+sqrt%28100%29
d+=+10
The distance from R to S is 10