A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis.

Question

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

(1 point)
Responses

11
11

8.54
8.54

73
73

7.62

Answer 1

To find the distance between the two points \( A(2, -3) \) and \( B(5, 5) \) using the Pythagorean Theorem, we can calculate the distance \( d \) using the formula:

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

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

First, calculate the differences in the coordinates:

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

Now, plug these values into the distance formula:

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

Using a calculator to evaluate \( \sqrt{73} \):

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

Thus, the length between the two points, rounded to the nearest hundredth, is:

8.54