How do you find the missing coordinate if the 1st coordinate is (2, 3) and the midpoint is (2, 5)?

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Answer 1 · 2016-08-08T12:31:12

The point is #(2,7)#

The formula to find the midpoint of a line is:

#M((x_1+x_2)/2 ; (y_1+y_2)/2) # and we have #M(2,5)#

We do not even need to do any calculation to find the #x#-value, because we notice that both points have an #x#-value of 2.

The line is therefore a vertical line and the missing endpoint will also have #x = 2#

But, to prove it:
# (2+x_2)/2 = 2 " "rArr 2+x_2 = 4 " "rArr x_2 = 2#

#(3+y_2)/2 = 5 " "rArr 3+y_2 = 10 " " y_2 = 7#

We could also have just asked the question..
"3 is halfway between 3 and what other number?"

The point is #(2,7)#