How do you find the coordinates of the other endpoint of a segment with the given Midpoint: (-4,6) and first Point: (-4,9)?

2 Answers
Alan P.
Jul 28, 2016

The other endpoint is at #(-4,3)#

Explanation:

The line segment passing through #(-4,9)# and #(-4,6)# is a vertical line with the midpoint #3# units below the first point.
The other endpoint must be #3# further units below the midpoint
i.e. at #(-4,(6-3))#

EZ as pi
Jul 28, 2016

Other endpoint is #(-4,3)#

Explanation:

We could substitute the values we have into the the Midpoint formula. We will then be able to solve for the missing values.

#M((x_1+x_2)/2 ; (y_1 +y_2)/2) = (-4,6)#

However, we should notice that the x-values are the same..
This means this is a vertical line. The other end of the line segment is therefore on the same line. #x=-4#

The distance from the top endpoint to the midpoint is #9-6 = 3#

The other endpoint will therefore be 3 units below the midpoint.
#y = 3#

Other endpoint is #(-4,3)#

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