A line segment on the coordinate plane has endpoints (2,4) and (4,y) and the midpoint of the segment is point (3,7), What is the value of y?

1 Answer
May 17, 2015

There are a few ways in which to do this sum, like for example you could use two points and find the equation of the line and then solve for #y# at the point #(4,y)# or we could use the midpoint formula.
which is:

#M = ((x_1 + x_2)/2 , (y_1 + y_2)/2)#

Which we are given #M# to be #(3,7)#

So we can put in the information we know into the formula

#(3,color(red)7) = ((2+4)/2,color(red)((4+y_2)/2))#

which we can observe that we need to solve for:

#(4 + y_2)/2 = 7#

Which gives us:

#4 + y_2 = 14#

#y_2 = 10# which is the answer to our question.

thus our end point will be #(4,color(red)10)#