The Midpoint: Average the Coordinates
The midpoint of (x1,y1) and (x2,y2) is just their coordinate-wise average.
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -5 | -5 |
| -4 | -4 |
| -3 | -3 |
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Make the line pass through the midpoint of (2, 4) and (6, 8). The midpoint is (4, 6).
- Make the line pass through the midpoint of (-2, 5) and (8, -1). The midpoint is (3, 2).
- The midpoint of (0, 2) and (4, 4) is (2, 3) — average the x values, average the y values. Pass through it.
- Now also through the midpoint of (2, −3) and (8, 3), which is (5, 0).
Check yourself
The midpoint of (a, b) and (c, d) is:
- ((a+c)/2, (b+d)/2) — coordinate-wise average. — correct
- ((a-c)/2, (b-d)/2) — coordinate-wise difference.
- ((ac)/2, (bd)/2) — coordinate-wise product.
- ((a+b)/2, (c+d)/2) — wrong pairing of x and y.
Think about it
- The midpoint of (2, 4) and (6, 8) lies on the line. Predict the midpoint, then slide to make the line pass through it.