Step by step
The question
Question: find the distance between (−2, 1) and (1, 5).
1 Plot the points
Draw the grid.
Put both points on the grid: (−2, 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 = −2 to x = 1 is 3.
We call it a = 3.
Then go up.
From y = 1 to y = 5 is 4.
We call it b = 4.
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 = 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 (−2, 1).
1 minus −2 is 3.
Taking away a negative is adding.
5 minus 1 is 4.
The same as on the grid.
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.