Question Video: Finding the Coordinates of a Point Using the Midpoint Formula Mathematics • 11th Grade

Video Transcript

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.