Step by step
The question
Question: find the distance between (0, 0) and (2, 4).
1 Plot the points
Draw the grid.
Put both points on the grid: (0, 0)
and (2, 4).
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 = 2 is 2.
We call it a = 2.
Then go up.
From y = 0 to y = 4 is 4.
We call it b = 4.
Across and up 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 = 2 and b = 4.
2² means 2 times 2.
That is 4.
4² means 4 times 4.
That is 16.
Write the squares: 4 + 16 = d².
4 plus 16 is 20.
d² is 20.
So d is the square root of 20.
20 is not a square number.
So we keep √20.
That is the exact answer.
With a calculator, √20 is about 4.5, 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 (2, 4) and (0, 0).
2 minus 0 is 2.
4 minus 0 is 4.
The same as on the grid.
4 plus 16 is 20.
We get √20 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.