Are they in a straight line?
Use the distance formula to check if three points are collinear without graphing.
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Find m and c so the line passes through (1, 2) and (3, 6)
- Verify if (2, 4) lies on this same line
- Three new points to test: (0, −1), (4, 11) and (2, 5). Pin the line to the first one.
- Now make it reach (4, 11) as well. If (2, 5) then lands on the same line, all three are collinear.
Check yourself
Three points A, B, and C are collinear if...
If AB = 5, BC = 7, and AC = 11, are the points collinear?
- The sum of the two smaller distances equals the largest distance (e.g., AB + BC = AC). — correct
- The distance from A to B is equal to the distance from B to C.
- The product of the distances AB * BC equals the distance AC.
- The slopes of AB and BC are equal, regardless of distance.
- Yes, because 5 + 7 = 12 which is close to 11.
- No, because 5 + 7 = 12, which is not equal to 11. — correct
- Yes, because all three distances are positive.
- No, because the largest distance is not double the smallest.
Think about it
- If we move point C so it's not on the line, what happens to the sum of distances AB + BC compared to AC?