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
73

Answer 1

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

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

For points \( A(2, -3) \) and \( B(5, 5) \):

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

Now substitute these values into the distance formula:

\[
d = \sqrt{(5 - 2)^2 + (5 - (-3))^2}
\]
\[
d = \sqrt{(3)^2 + (5 + 3)^2}
\]
\[
d = \sqrt{9 + 8^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]

Now we calculate \( \sqrt{73} \):

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

Rounded to the nearest hundredth, this is approximately \( 8.54 \).

Thus, the distance between points A and B is \( \boxed{8.54} \).