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

5.57
5.57

9

Answer 1

To find the length between the two points (-2, -1) and (2, 4), we can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given points, we can plug in the values:
d = √((2 - (-2))^2 + (4 - (-1))^2)
= √((4 + 2)^2 + (4 + 1)^2)
= √(6^2 + 5^2)
= √(36 + 25)
= √61
≈ 7.81

Rounding to the nearest hundredth, the length between the two points is approximately 7.81.