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

1 answer

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