Definition: The distance between two points on a coordinate plane is found by treating them as ends of a hypotenuse and applying the Pythagorean theorem.
How do you find distance between points?
Build a right triangle. The horizontal leg has length |x2 – x1| and the vertical leg has length |y2 – y1|. The segment joining the points is the hypotenuse.
What is the formula?
d = the square root of [(x2 – x1)2 + (y2 – y1)2].
What does an example look like?
Find the distance from A(-2, 3) to B(4, 11). The horizontal change is 6 and the vertical change is 8. Then d is the square root of 36 + 64 = 100, so d = 10.
What if the points line up?
Then one leg is zero, and you just count: from (5, -1) to (5, 7) the distance is 8.
Where is it used?
A delivery robot moves from (1, 1) to (9, 16) on a grid. The change is 8 by 15, and the straight-line distance is the square root of 64 + 225 = 289, or 17 units.
What is a common mistake?
Forgetting to take the square root at the end, or subtracting x from y. Pair the x-values together and the y-values together.