Question

Find the distance between the points (-4,-5) and (1,-2).

7
4.7
5.4
9.2

Answer 1

To find the distance between the points \((-4, -5)\) and \((1, -2)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-4, -5)\) and \((x_2, y_2) = (1, -2)\).

Now substituting the values into the formula:

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

Calculating the differences:

\[
x_2 - x_1 = 1 - (-4) = 1 + 4 = 5
\]
\[
y_2 - y_1 = -2 - (-5) = -2 + 5 = 3
\]

Now substitute these differences into the distance formula:

\[
d = \sqrt{(5)^2 + (3)^2} = \sqrt{25 + 9} = \sqrt{34}
\]

Now we can approximate \(\sqrt{34}\):

\[
\sqrt{34} \approx 5.83
\]

Given the options:

- 7
- 4.7
- 5.4
- 9.2

The closest approximation (not explicitly listed) is typically around 5.8, but since it's not in the options, if we must select the closest value from the options given, we choose:

**7.**