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
8.54
8.54
73
73
7.62
7.62
11
11
Skip to navigation
To find the length between two points using the Pythagorean Theorem, we need to find the length of the two legs of a right triangle formed by the two points and the origin.
The length of one leg is the difference in the x-coordinates: 5 - 2 = 3.
The length of the other leg is the difference in the y-coordinates: 5 - (-3) = 8.
Using the Pythagorean Theorem, the length of the hypotenuse (distance between the two points) is:
c^2 = 3^2 + 8^2
c^2 = 9 + 64
c^2 = 73
c ≈ √73 ≈ 8.54
So, the length between the two points is approximately 8.54.