What is the distance between the points (3, 4) and (6, 8)?

To find the distance between the two points (3, 4) and (6, 8), we can use the distance formula, which is derived from the Pythagorean theorem. The formula is given by:

[

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

]

In this case, the coordinates are:

• ( (x_1, y_1) = (3, 4) )

• ( (x_2, y_2) = (6, 8) )

Substituting the values into the formula:

[

d = \sqrt{(6 - 3)^2 + (8 - 4)^2}

]

Calculating each part step-by-step:

1. Calculate ( x_2 - x_1 ):

[

6 - 3 = 3

]

2. Calculate ( y_2 - y_1 ):

[

8 - 4 = 4

]

3. Now, substitute these results back into the formula:

[

d = \sqrt{(3)^2 +