Math 1 · Unit 11 · Lesson 2 · part 2 of 4
Halfway across and halfway up
Three tools, three questions: how steep (slope), how long (distance), where is the middle (midpoint).
Halfway across and halfway up
Three tools, three questions: how steep (slope), how long (distance), where is the middle (midpoint). This lesson is where is the middle. The midpoint is the point exactly halfway along a segment. It bisects the segment, cutting it into two equal pieces, a 1 to 1 ratio: the two halves are the same length.
Start on a number line. Halfway between 2 and 8 is 5. How do you get 5? Add the two numbers and divide by 2: 2 + 82 = 102 = 5. That is the mean, also called the average. The midpoint of two numbers is their average.
On the grid, do it in each direction separately. Halfway across is the average of the x's. Halfway up is the average of the y's.
Jennifer is at (9, 7) and Jane is at (15, 9). They agree to meet in the middle. Across: 9 + 152 = 242 = 12. Up: 7 + 92 = 162 = 8. They meet at (12, 8).
Do it from Jane's end instead: 15 + 92 = 12 and 9 + 72 = 8. The same point, because adding in either order gives the same sum. The order of the endpoints does not matter.
Drag either endpoint and watch the midpoint move. The two halves always have the same length.