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
A
7.62
B
8.54
C
11
D
73

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length between point A and point B, we can use the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the horizontal distance between point A and point B is 3 units (5 - 2) and the vertical distance is 8 units (5 - (-3)).

Using the Pythagorean Theorem, we can calculate:

Hypotenuse^2 = 3^2 + 8^2
Hypotenuse^2 = 9 + 64
Hypotenuse^2 = 73

To find the length of the hypotenuse (the distance between point A and point B), we take the square root of 73:

Hypotenuse ≈ √73 ≈ 8.54

Therefore, the length between point A and point B is approximately 8.54 units.

The correct answer is B) 8.54.