Question

Find the distance between the points (6,3) and (0,4).
Write your answer as a whole number or a fully simplified radical expression. Do not round.

Answer 1

To find the distance between the points \( (6, 3) \) and \( (0, 4) \), we can use the distance formula:

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

Here, let \( (x_1, y_1) = (6, 3) \) and \( (x_2, y_2) = (0, 4) \). Plugging in these coordinates into the formula:

\[
d = \sqrt{(0 - 6)^2 + (4 - 3)^2}
\]

Calculating the differences:

\[
0 - 6 = -6 \quad \text{and} \quad 4 - 3 = 1
\]

Now substitute these values into the formula:

\[
d = \sqrt{(-6)^2 + (1)^2}
\]

Calculating the squares:

\[
(-6)^2 = 36 \quad \text{and} \quad (1)^2 = 1
\]

Now add them together:

\[
d = \sqrt{36 + 1} = \sqrt{37}
\]

Thus, the distance between the points \( (6, 3) \) and \( (0, 4) \) is

\[
\boxed{\sqrt{37}}
\]