Step by step
The question
Question: find the distance between (−6, −2) and (−1, −4).
1 Plot the points
Draw the grid.
Put both points on the grid: (−6, −2)
and (−1, −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 = −6 to x = −1 is 5.
We call it a = 5.
Then go down.
From y = −2 to y = −4 is 2.
A length is never negative.
So b = 2.
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 = 5 and b = 2.
5² means 5 times 5.
That is 25.
2² means 2 times 2.
That is 4.
Write the squares: 25 + 4 = d².
25 plus 4 is 29.
d² is 29.
So d is the square root of 29.
29 is not a square number.
So we keep √29.
That is the exact answer.
With a calculator, √29 is about 5.4, 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 (−1, −4) and (−6, −2).
−1 minus −6 is 5.
Taking away a negative is adding.
−4 minus −2 is −2.
Taking away a negative is adding.
Careful: (−2)² is −2 times −2.
Minus times minus is plus: 4, not −4.
25 plus 4 is 29.
We get √29 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.