Distance from (0,0) to (3,4)
Use the distance formula to find the length of a line segment starting at the origin.
Equation
y = sqrt(x^2 + 1^2)
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 1.41 |
| 2 | 2.24 |
| 3 | 3.16 |
| 4 | 4.12 |
| 5 | 5.1 |
| 6 | 6.08 |
What this lesson covers
What you do
You shape the function y = sqrt(x^2 + b^2) and watch the graph answer.
Challenges to clear
- Set b = 4. At x = 3 the distance is 5 — the famous 3-4-5 right triangle.
- At x = 0 the distance is just b itself: 4 straight up from the origin.
- A bigger right triangle. The vertical leg is 12 — slide b there first.
- Now slide c to your guess at the distance, until the difference reads 0 at x = 5. √(5² + 12²) = 13 — the other famous triple.
Check yourself
Why can't we just add 3 and 4 to get the distance?
If you change b to 3 and x to 4, is the distance still 5? What about b=5 and x=12?
- Because distance is a straight line (hypotenuse), not the sum of horizontal and vertical steps. — correct
- Because 3 + 4 = 7, which is wrong.
- Because we must use the square root.
- Because the formula is too complicated for simple addition.
- Yes, distance is 5 for (4,3). For (12,5), distance is 13 (5-12-13 triangle). — correct
- No, distance changes for (4,3). For (12,5), distance is 17.
- Yes, distance is 5 for (4,3). For (12,5), distance is 17.
- No, distance changes for (4,3). For (12,5), distance is 13.
Think about it
- d = √(x² + b²) with x = 3 and b = 4. What is d?