Question

B: (5, 5)
A: (2, -3)

Apply the Pythagorean theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.

73

8.54

7.62

11

Answer 1

To find the distance between the two points \( B(5, 5) \) and \( A(2, -3) \), we can use the distance formula 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 points A and B:

- \( x_1 = 2 \), \( y_1 = -3 \)
- \( x_2 = 5 \), \( y_2 = 5 \)

Now plug the values into the distance formula:

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

Calculating the differences:

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

Calculating the squares:

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

Now we will calculate the square root of 73:

\[
\sqrt{73} \approx 8.54
\]

Thus, the length between the two points \( B(5, 5) \) and \( A(2, -3) \) is approximately **8.54** when rounded to the nearest hundredth.

So the answer is **8.54**.