Question

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?

Answer 1

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)`