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 (2, -3), and point B at (5, 5).

Apply the pythagorean theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The distance between two points in a plane can be found using the Pythagorean Theorem, which states that for 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 two points A and B form the endpoints of a right triangle, with the line connecting them being the hypotenuse. The x-coordinate of point A is 2, the y-coordinate of point A is -3, the x-coordinate of point B is 5, and the y-coordinate of point B is 5.

Using the Pythagorean Theorem, we can calculate the distance between point A and point B:

d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((5 - 2)^2 + (5 - (-3))^2)
d = √(3^2 + 8^2)
d = √(9 + 64)
d = √73
d ≈ 8.54

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