Question

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

9
9

6:40
6:40

5.57

Answer 1

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

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

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

Now, let's plug in the values:

1. Calculate \(x_2 - x_1\): \[ 2 - (-2) = 2 + 2 = 4 \]

2. Calculate \(y_2 - y_1\): \[ 4 - (-1) = 4 + 1 = 5 \]

3. Now apply these to the distance formula: \[ d = \sqrt{(4)^2 + (5)^2} = \sqrt{16 + 25} = \sqrt{41} \]

Finally, we need to find the approximate value of \(\sqrt{41}\): \[ \sqrt{41} \approx 6.403124237 \]

Rounding to the nearest hundredth, the distance \(d\) is approximately \(6.40\).

So, the correct answer is: 6:40