Step by step
The question
Question: find the distance between (−3, −3) and (2, 9).
1 Plot the points
Draw the grid.
Put both points on the grid: (−3, −3)
and (2, 9).
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 = −3 to x = 2 is 5.
We call it a = 5.
Then go up.
From y = −3 to y = 9 is 12.
We call it b = 12.
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 = 5 and b = 12.
5² means 5 times 5.
That is 25.
12² means 12 times 12.
That is 144.
Write the squares: 25 + 144 = d².
25 plus 144 is 169.
d² is 169.
So d is the square root of 169.
13 times 13 is 169.
So d = 13.
The distance is 13.
4 Check
Let's check with the distance formula.
It does the same steps in one line.
Put in the numbers of (2, 9) and (−3, −3).
2 minus −3 is 5.
Taking away a negative is adding.
9 minus −3 is 12.
Taking away a negative is adding.
The same as on the grid.
25 plus 144 is 169.
The square root is 13 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.