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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

73
73

8.54
8.54

7.62
7.62

11

Answer 1

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

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

Here, the coordinates for point A are \( (x_1, y_1) = (2, -3) \) and for point B are \( (x_2, y_2) = (5, 5) \).

Plugging in the values:

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

Now, calculating \( \sqrt{73} \):

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

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

The answer is:

8.54