A line segment has an endpoint at (4, 6), the midpoint of the line segment is (1, 5). What are the coordinates of the point at the other end of the line segment?

1 Answer
LizZ
Feb 27, 2018

The other end is at #(-2,4)#.

Explanation:

I think about this by drawing a picture of the two points, no accuracy necessary, and putting a right triangle with its hypotenuse along the line.
I look at the change in each of the #x# and #y# directions. From the given endpoint to the midpoint, the segment moves #-3# in the #x# direction and #-1# in the #y# direction.
To find the other endpoint, just move the same way from the midpoint. From #(1,5)#: #(1-3,5-1)=(-2,4).#

Here's my sketch too: enter image source here

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