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

6:40
6:40

41
41

9
9

5.57

Answer 1

To find the length between the two points (-2, -1) and (2, 4), we can use the Pythagorean Theorem.

First, we find the difference in x-coordinates by subtracting the x-coordinate of the first point from the x-coordinate of the second point:

2 - (-2) = 4

Then, we find the difference in y-coordinates by subtracting the y-coordinate of the first point from the y-coordinate of the second point:

4 - (-1) = 5

Now, we have the lengths of the two legs of a right triangle. To find the length of the hypotenuse (which is the distance between the two points), we can use the Pythagorean Theorem:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the two legs.

Plugging in the values we found:

c^2 = 4^2 + 5^2

c^2 = 16 + 25

c^2 = 41

Taking the square root of both sides to find c:

c = sqrt(41)

Rounding to the nearest hundredth, the length between the two points is approximately 6.40.