Step by step
The question
Question: find the distance between (−1, 4) and (5, −4).
1 Plot the points
Draw the grid.
Put both points on the grid: (−1, 4)
and (5, −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 = −1 to x = 5 is 6.
We call it a = 6.
Then go down.
From y = 4 to y = −4 is 8.
A length is never negative.
So b = 8.
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 = 6 and b = 8.
6² means 6 times 6.
That is 36.
8² means 8 times 8.
That is 64.
Write the squares: 36 + 64 = d².
36 plus 64 is 100.
d² is 100.
So d is the square root of 100.
10 times 10 is 100.
So d = 10.
The distance is 10.
4 Check
Let's check with the distance formula.
It does the same steps in one line.
Put in the numbers of (5, −4) and (−1, 4).
5 minus −1 is 6.
Taking away a negative is adding.
−4 minus 4 is −8.
Careful: (−8)² is −8 times −8.
Minus times minus is plus: 64, not −64.
36 plus 64 is 100.
The square root is 10 again.
Right!
Let's look back.
First: plot the points.
Then: make a right triangle.
Then: use a² + b² = c².
Last: check.