On the graph, which point is
halfway between one, eight and five, two?
We have the point one, eight — we
could call it 𝐴 — and the point five, two — we can call 𝐵. And we want to know which point is
halfway between the two points. The point halfway between these two
points is called the midpoint. And to find the midpoint, we
average the 𝑥-coordinates of the two endpoints. And then, we average the
𝑦-coordinates of the two endpoints. So, we’ll let point 𝐴 be 𝑥 one,
𝑦 one and point 𝐵 be 𝑥 two, 𝑦 two. Then to find the midpoint, we add
one plus five and divide by two. And then, we add eight plus two and
divide by two. This gives us six over two and 10
over two, which we reduce to three, five.
On the graph, the coordinate three,
five is here. And if we look at this point, we
see from 𝐵 that is up three and left two. And then, if we want to go from the
midpoint to point 𝐴, again, we have up three and left two. This confirms that the distance
from 𝐴 to the midpoint is the same as the distance from the midpoint to 𝐵. Halfway between one, eight and
five, two is the point three, five.