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
5.57
5.57
9
9
6:40
To find the distance between the two points, we can use the distance formula or apply the Pythagorean theorem.
The distance formula is derived from the Pythagorean theorem, so in this case, we can use the Pythagorean theorem directly to find the length between the two points.
Using the Pythagorean theorem, the length between the two points is equal to the square root of the sum of the squares of the differences in x-coordinates and y-coordinates.
In this case, the x-coordinates of the two points are -2 and 2, and the y-coordinates are -1 and 4.
The difference in x-coordinates is 2 - (-2) = 4.
The difference in y-coordinates is 4 - (-1) = 5.
Applying the Pythagorean theorem:
Length = sqrt((difference in x-coordinates)^2 + (difference in y-coordinates)^2)
Length = sqrt(4^2 + 5^2)
Length = sqrt(16 + 25)
Length = sqrt(41)
Rounding to the nearest hundredth, the length between the two points is approximately 6.40.