Given point 𝐴 has coordinates
four, eight and 𝐵 has coordinates six, six, what are the coordinates of the
midpoint of line segment 𝐴𝐵?
We can solve this problem
graphically or by using the midpoint formula. And it is this method we’ll use
first. We recall that if points 𝐴 and 𝐵
have coordinates 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two, respectively, then the midpoint
has coordinates 𝑥 one plus 𝑥 two over two, 𝑦 one plus 𝑦 two over two. In this question, point 𝐴 has
coordinates four, eight, and point 𝐵 has coordinates six, six. This means that the midpoint of the
line segment 𝐴𝐵 has 𝑥-coordinate equal to four plus six over two and
𝑦-coordinate equal to eight plus six over two. Adding four and six gives us
10. And dividing this by two gives us
five. Likewise, eight plus six is equal
to 14. And dividing this by two gives us
seven. The midpoint of points 𝐴 and 𝐵
has coordinates five, seven.
As already mentioned, we could also
represent this graphically on the two-dimensional coordinate plane. The midpoint of line segment 𝐴𝐵
lies halfway between points 𝐴 and 𝐵 as shown. And it is clear from the graph that
this lies at the point five, seven.