Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary. A(2 -3) B(5,5)
1. 11
2. 73
3. 7.62
4. 8.54

Answer 1

To find the distance between the two points \( A(2, -3) \) and \( B(5, 5) \), we can use the distance formula, which is derived from the Pythagorean Theorem:

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

Here, the coordinates of point \( A \) are \( (x_1, y_1) = (2, -3) \) and those of point \( B \) are \( (x_2, y_2) = (5, 5) \).

Now we can substitute the coordinates into the formula:

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

Calculating the differences:

\[
= \sqrt{(3)^2 + (5 + 3)^2}
\]
\[
= \sqrt{(3)^2 + (8)^2}
\]

Now computing the squares:

\[
= \sqrt{9 + 64}
\]
\[
= \sqrt{73}
\]

Now, we need to find the square root of 73, which is approximately:

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

Rounding to the nearest hundredth gives us:

\[
\approx 8.54
\]

Thus, the length between the two points is:

**4. 8.54**