SOLUTION: Find the other endpoint of the line segment that has the given endpoint and midpoint Endpoint (2,1), midpoint (4,4)

Question 1200003: Find the other endpoint of the line segment that has the given endpoint and midpoint
Endpoint (2,1), midpoint (4,4)
Found 2 solutions by htmentor, greenestamps:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The midpoint m of a line segment (x1,y1) (x2,y2) = ((x1+x2)/2, (y1+y2)/2)
(2+x)/2 = 4 -> x = x = 6
(1+y)/2 = 4 -> y = 7
Ans: (6,7)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The very formal algebraic solution shown by the other tutor is of course fine; and perhaps it is what the student was expected to do.

However, for UNDERSTANDING why the answer is what it is, this is one kind of problem where I think a solution using logical reasoning and very simple arithmetic is of more use to the student.

When going from one endpoint of a segment to the midpoint, you have gone half of the distance to the other endpoint. So to find the other endpoint, find how far you have gone in each of the x and y directions to get from the given endpoint to the midpoint, and then go those same distances in each direction starting from the midpoint to get to the other endpoint.

x coordinate: from 2 to 4 is a change of 2, so I need to go 2 more; 4+2=6

y coordinate: from 1 to 4 is a change of 3, so I need to go 3 more; 4+3=7

ANSWER: (6,7)

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