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Question 1094717: Find the coordinates of R if N(8, -3) is the midpoint of RS and S has coordinates (-1, 5).
Found 2 solutions by greenestamps, josmiceli:
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
Draw a rough sketch if it helps; but forget the formal midpoint formula or any other algebra and use common sense.
Imagine starting at S, where you know the coordinates are (-1,5). You walk along segment RS, and you reach the midpoint N, with coordinates (8,-3).
You know you have reached the midpoint; that means you are halfway. And that means the distance you have left to walk is the same as the distance you just walked.
You just walked from a point with x coordinate -1 to a point with x coordinate 8; that is 9 units. You need to go another 9 units in the x direction to get to the end of your walk, at point R. 8+9=17; the x coordinate of R is 17.
Similarly, you just walked from a y coordinate of 5 to a y coordinate of -3, a change of -8. You need to walk another -8 units in the y direction to reach R; the y coordinate of R is -3-8 = -11.
R is (17,-11).
All the words make this look like a lot of work. But without the words, it's a lot faster than plugging numbers into some magic formula:
x: from -1 to 8 is 9; 8 plus 9 more is 17
y: from 5 to -3 is -8; -3 plus another -8 makes -11
or...
8-(-1) = 9; 8+9 = 17;
(-3)-5 = -8; -3-8 = -11
Answer by josmiceli(19441)  (Show Source):
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