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

Question

1610 views around the world

You can reuse this answer
Creative Commons License

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)#