How do you calculate the distance from (2, 2) to (5, 6)?

To calculate the distance from (2, 2) to (5, 6), use the distance formula derived from Pythagoras' theorem.

The distance formula is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. For our points, \((x_1, y_1) = (2, 2)\) and \((x_2, y_2) = (5, 6)\).

First, find the differences in the x-coordinates and y-coordinates:
\[ x_2 - x_1 = 5 - 2 = 3 \]
\[ y_2 - y_1 = 6 - 2 = 4 \]

Next, square these differences:
\[ (x_2 - x_1)^2 = 3^2 = 9 \]
\[ (y_2 - y_1)^2 = 4^2 = 16 \]

Then, add these squared differences together:
\[ 9 + 16 = 25 \]

Finally, take the square root of this sum to find the distance:
\[ \sqrt{25} = 5 \]

So, the distance from (2, 2) to (5, 6) is 5 units. This method ensures you accurately measure the straight-line distance between any two points on a coordinate plane.