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
5.57
5.57
41
41
9
9
6:40
6:40
To find the distance between two points using the Pythagorean Theorem, we need to find the differences in the x-coordinates and y-coordinates and substitute them into the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates are:
Point 1: (-2, -1)
Point 2: (2, 4)
The differences in the x-coordinates and y-coordinates are:
Δx = 2 - (-2) = 4
Δy = 4 - (-1) = 5
Now we can substitute these values into the formula:
d = √((4)^2 + (5)^2) = √(16 + 25) = √41
Rounded to the nearest hundredth, the length between the two points is approximately 6.40.
So the correct answer is 6.40.