Distance and the Pythagorean Theorem Quick Check
4 of 54 of 5 Items
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. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
41
41
6:40
6:40
9
9
5.57
5.57
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To find the length between two points using the Pythagorean Theorem, we need to find the distance between the x-coordinates and the distance between the y-coordinates, and then use these values to calculate the hypotenuse of a right triangle.
The x-coordinate of the first point is -2, and the x-coordinate of the second point is 2. The distance between these two points on the x-axis is 2 - (-2) = 4.
The y-coordinate of the first point is -1, and the y-coordinate of the second point is 4. The distance between these two points on the y-axis is 4 - (-1) = 5.
Now we can use the Pythagorean Theorem to find the length between the two points:
Length = √(distance on x-axis)^2 + (distance on y-axis)^2
Length = √(4)^2 + (5)^2
Length = √16 + 25
Length = √41
Rounding to the nearest hundredth, the length between the two points is approximately 6.40.
Therefore, the correct answer is 6.40.