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
73
Skip to navigation
To find the length between the two points A and B, we can use the formula for the distance between two points in a coordinate plane, which is based on the Pythagorean theorem.
The formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of point A are (2, -3) and the coordinates of point B are (5, 5).
Substituting these values into the formula, we have:
d = √((5 - 2)^2 + (5 - (-3))^2)
= √(3^2 + 8^2)
= √(9 + 64)
= √73
Rounding to the nearest hundredth, the length between points A and B is approximately 8.54.
Therefore, the correct answer is:
8.54