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)

Answer 1

To find the length 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 given by the formula:

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

First, we identify our points:
- \(x_1 = -2\), \(y_1 = -1\)
- \(x_2 = 2\), \(y_2 = 4\)

Now, we calculate the differences in the coordinates:

\[
x_2 - x_1 = 2 - (-2) = 2 + 2 = 4
\]

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

Now we can substitute these values into the distance formula:

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

Finally, we can approximate \(\sqrt{41}\).

Calculating \(\sqrt{41} \approx 6.403124237\).

Rounding to the nearest hundredth, the distance \(d\) is approximately:

\[
\boxed{6.40}
\]