Step by step
The question
Question: find the distance between (−4, −1) and (−1, −5).
1 Plot the points
Draw the grid.
Put both points on the grid: (−4, −1)
and (−1, −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 = −4 to x = −1 is 3.
We call it a = 3.
Then go down.
From y = −1 to y = −5 is 4.
A length is never negative.
So b = 4.
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 = 3 and b = 4.
3² means 3 times 3.
That is 9.
4² means 4 times 4.
That is 16.
Write the squares: 9 + 16 = d².
9 plus 16 is 25.
d² is 25.
So d is the square root of 25.
5 times 5 is 25.
So d = 5.
The distance is 5.
4 Check
Let's check with the distance formula.
It does the same steps in one line.
Put in the numbers of (−1, −5) and (−4, −1).
−1 minus −4 is 3.
Taking away a negative is adding.
−5 minus −1 is −4.
Taking away a negative is adding.
Careful: (−4)² is −4 times −4.
Minus times minus is plus: 16, not −16.
9 plus 16 is 25.
The square root is 5 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.