Step by step
The question
Question: find the distance between (1, 2) and (3, 5).
1 Plot the points
Draw the grid.
Put both points on the grid: (1, 2)
and (3, 5).
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 = 1 to x = 3 is 2.
We call it a = 2.
Then go up.
From y = 2 to y = 5 is 3.
We call it b = 3.
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 = 3.
2² means 2 times 2.
That is 4.
3² means 3 times 3.
That is 9.
Write the squares: 4 + 9 = d².
4 plus 9 is 13.
d² is 13.
So d is the square root of 13.
13 is not a square number.
So we keep √13.
That is the exact answer.
With a calculator, √13 is about 3.6, 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 (3, 5) and (1, 2).
3 minus 1 is 2.
5 minus 2 is 3.
The same as on the grid.
4 plus 9 is 13.
We get √13 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.