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

9
9

41
41

5.57
5.57

6:40

1 answer

To find the distance between the two points \((-2, -1)\) and \((2, 4)\), we can use the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of the points:

  • \(x_1 = -2\)
  • \(y_1 = -1\)
  • \(x_2 = 2\)
  • \(y_2 = 4\)

We calculate \(d\):

\[ d = \sqrt{(2 - (-2))^2 + (4 - (-1))^2} \] \[ d = \sqrt{(2 + 2)^2 + (4 + 1)^2} \] \[ d = \sqrt{(4)^2 + (5)^2} \] \[ d = \sqrt{16 + 25} \] \[ d = \sqrt{41} \]

Calculating \(\sqrt{41}\), we get:

\[ d \approx 6.403124237 \]

Rounding to the nearest hundredth:

\[ d \approx 6.40 \]

Thus, the answer is:

6.40