Question

what is the length between (3,2) and (7,8) on an x y graph.

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.



7.21

51.98

6.25

62.25

Answer 1

To find the distance between the points \((3, 2)\) and \((7, 8)\) on an xy-graph, we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting the coordinates of the points \((3, 2)\) and \((7, 8)\):

- \(x_1 = 3\)
- \(y_1 = 2\)
- \(x_2 = 7\)
- \(y_2 = 8\)

Now plug in these values into the formula:

\[
d = \sqrt{(7 - 3)^2 + (8 - 2)^2}
\]
\[
d = \sqrt{(4)^2 + (6)^2}
\]
\[
d = \sqrt{16 + 36}
\]
\[
d = \sqrt{52}
\]

Now we can calculate \(\sqrt{52}\):

\[
d \approx 7.2111
\]

Rounding this to the nearest hundredth, we get:

\[
d \approx 7.21
\]

So, the distance between the points (3, 2) and (7, 8) is **7.21**.