Question

Use the image to answer the question.

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.

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

7.62
7.62

8.54
8.54

73

Answer 1

To find the distance between the two points \( A(2, -3) \) and \( B(5, 5) \), we can use the Pythagorean Theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:

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

Plugging in the coordinates of points A and B:

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

Calculating the differences:

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

Now, substitute these values into the distance formula:

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

Calculating the square root of 73:

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

Rounding to the nearest hundredth, the distance between the two points is approximately \( 8.54 \).

The answer is:

**8.54**