Step by step
The question
Question: find the distance between (1, 1) and (4, 2).
1 Plot the points
Draw the grid.
Put both points on the grid: (1, 1)
and (4, 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 = 1 to x = 4 is 3.
We call it a = 3.
Then go up.
From y = 1 to y = 2 is 1.
We call it b = 1.
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 = 3 and b = 1.
3² means 3 times 3.
That is 9.
1² means 1 times 1.
That is 1.
Write the squares: 9 + 1 = d².
9 plus 1 is 10.
d² is 10.
So d is the square root of 10.
10 is not a square number.
So we keep √10.
That is the exact answer.
With a calculator, √10 is about 3.2, 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 (4, 2) and (1, 1).
4 minus 1 is 3.
2 minus 1 is 1.
The same as on the grid.
9 plus 1 is 10.
We get √10 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.