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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

6.40
6.40

9

Answer 1

To find the distance between the two points \((-2, -1)\) and \((2, 4)\) using the Pythagorean Theorem, we can use the distance formula:

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

Here, \((x_1, y_1) = (-2, -1)\) and \((x_2, y_2) = (2, 4)\).

Plugging the coordinates into the formula:

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

Calculating the differences:

\[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \] \[ y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \]

Now substituting these values back into the formula:

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

Calculating \(\sqrt{41}\):

\[ \sqrt{41} \approx 6.40 \]

So the length between the two points is approximately \(6.40\).

The rounded answer to the nearest hundredth is:

6.40