Question

Apply the Pythagorean Theorem to find the length between the two points (-2, -1) and (2, 4). Round to the nearest hundredth, if necessary.
A. 6:40
B. 9
C. 5.57
D. 41

Answer 1

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

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

Here, the coordinates are:
- \( (x_1, y_1) = (-2, -1) \)
- \( (x_2, y_2) = (2, 4) \)

Now, substitute the values into the formula:

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

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

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

4. Now, we can calculate \(\sqrt{41}\). The approximate value of \(\sqrt{41}\) (using a calculator) is about \(6.403\).

5. Finally, rounding to the nearest hundredth gives \(6.40\).

Thus, the correct answer is **A. 6:40** (written here as 6.40).