College Math Placement Practice Test

To find the distance between the two points (1, 2) and (4, 6), 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}

\]

Here, \((x_1, y_1) = (1, 2)\) and \((x_2, y_2) = (4, 6)\).

Now, we can substitute the values into the formula:

1. Calculate the differences in the x-coordinates and y-coordinates:

- \(x_2 - x_1 = 4 - 1 = 3\)

- \(y_2 - y_1 = 6 - 2 = 4\)

2. Plug these differences into the distance formula:

\[

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

\]

3. Simplify the squares:

\[

d = \sqrt{9 + 16} = \sqrt{25}

\]

4. The square root of 25 is:

\