Step by step
The question
Question: find the distance between (2, 5) and (6, 2).
1 Plot the points
Draw the grid.
Put both points on the grid: (2, 5)
and (6, 2).
The distance is the length of this line.
We call it d.
2 Make a right triangle
From the left point, go across.
From x = 2 to x = 6 is 4.
We call it a = 4.
Then go down.
From y = 5 to y = 2 is 3.
A length is never negative.
So b = 3.
Across and down make a right angle.
The distance d is the longest side.
3 Use a² + b² = c²
The rule for every right triangle: a² + b² = c².
Here c is the distance d.
Now put the numbers in: a = 4 and b = 3.
4² means 4 times 4.
That is 16.
3² means 3 times 3.
That is 9.
Write the squares: 16 + 9 = d².
16 plus 9 is 25.
d² is 25.
So d is the square root of 25.
5 times 5 is 25.
So d = 5.
The distance is 5.
4 Check
Let's check with the distance formula.
It does the same steps in one line.
Put in the numbers of (6, 2) and (2, 5).
6 minus 2 is 4.
2 minus 5 is −3.
Careful: (−3)² is −3 times −3.
Minus times minus is plus: 9, not −9.
16 plus 9 is 25.
The square root is 5 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.