Question

Find the distance between the points (7,3) and (10,5).
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 \((7,3)\) and \((10,5)\), we can use the distance formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Here, we have:

- \((x_1, y_1) = (7, 3)\)
- \((x_2, y_2) = (10, 5)\)

Now, we can substitute these values into the distance formula:

\[
d = \sqrt{(10 - 7)^2 + (5 - 3)^2}
\]

Calculating each part:

\[
x_2 - x_1 = 10 - 7 = 3
\]
\[
y_2 - y_1 = 5 - 3 = 2
\]

Now, substitute these results back into the distance formula:

\[
d = \sqrt{(3)^2 + (2)^2}
\]
\[
d = \sqrt{9 + 4}
\]
\[
d = \sqrt{13}
\]

The distance between the points \((7,3)\) and \((10,5)\) is

\[
\sqrt{13}
\]

This is a fully simplified radical expression.