Step by step
The question
Question: find the distance between (0, 5) and (5, 0).
1 Plot the points
Draw the grid.
Put both points on the grid: (0, 5)
and (5, 0).
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 = 0 to x = 5 is 5.
We call it a = 5.
Then go down.
From y = 5 to y = 0 is 5.
A length is never negative.
So b = 5.
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 = 5 and b = 5.
5² means 5 times 5.
That is 25.
5² means 5 times 5.
That is 25.
Write the squares: 25 + 25 = d².
25 plus 25 is 50.
d² is 50.
So d is the square root of 50.
50 is not a square number.
So we keep √50.
That is the exact answer.
With a calculator, √50 is about 7.1, to the nearest tenth.
4 Check
Let's check with the distance formula.
It does the same steps in one line.
Put in the numbers of (5, 0) and (0, 5).
5 minus 0 is 5.
0 minus 5 is −5.
Careful: (−5)² is −5 times −5.
Minus times minus is plus: 25, not −25.
25 plus 25 is 50.
We get √50 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.