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
11
11
8.54
8.54
73
73
7.62
7.62
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To find the length between two points on a graph, you can use the Pythagorean Theorem.
First, identify the coordinates of the two points. In this case, the coordinates are point A at (2, -3) and point B at (5, 5).
Next, calculate the difference between the x-coordinates and the y-coordinates of the two points.
For the x-coordinates:
5 - 2 = 3
For the y-coordinates:
5 - (-3) = 5 + 3 = 8
Now, use the differences calculated above to form a right triangle. The line connecting the two points will be the hypotenuse of this right triangle. The length of this line is the distance between the two points.
Apply the Pythagorean Theorem, which 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 our case:
Hypotenuse^2 = 3^2 + 8^2
Hypotenuse^2 = 9 + 64
Hypotenuse^2 = 73
Now, take the square root of both sides to find the length of the hypotenuse (the distance between the two points):
Hypotenuse = √73
And finally, round the answer to the nearest hundredth:
Hypotenuse ≈ 8.54
Therefore, the length between the two points, rounded to the nearest hundredth, is 8.54.