Question

Apply the Pythagorean Theorem to find the length between the two points (2, -3) and (5, 5). Round to the nearest hundredth, if necessary.

A. 7.62
B. 11
C. 73
D. 8.54

Answer 1

To find the length between the two points \((2, -3)\) and \((5, 5)\), 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:

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

Here, our points are \((x_1, y_1) = (2, -3)\) and \((x_2, y_2) = (5, 5)\).

First, we calculate the differences in the coordinates:

\[
x_2 - x_1 = 5 - 2 = 3
\]
\[
y_2 - y_1 = 5 - (-3) = 5 + 3 = 8
\]

Now we input these differences into the distance formula:

\[
d = \sqrt{(3)^2 + (8)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]

Next, we need to calculate \(\sqrt{73}\) and round it to the nearest hundredth:

\[
\sqrt{73} \approx 8.544
\]

Rounding this to the nearest hundredth gives us:

\[
d \approx 8.54
\]

So the answer is \( \boxed{8.54} \).