Question

Distance and the Pythagorean Theorem Quick Check
5 of 55 of 5 Items






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

7.62
7.62

11
11

8.54
8.54

73

Answer 1

To find the distance between the points A (2, -3) and B (5, 5) using the Pythagorean Theorem, you can use the distance formula, which is derived from the 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 the points A (2, -3) and B (5, 5):

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

Now, plug in the values:

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

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

\[
d \approx 8.54
\]

So, the length between the two points A and B is approximately **8.54**.

The correct answer is **8.54**.