Question

Find the distance of line F . Round your answer to the nearest tenth.
(-7,-4),(3,-6)

Answer 1

To find the distance between the two points \((-7, -4)\) and \((3, -6)\), we can use the distance formula:

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

Here, \( (x_1, y_1) = (-7, -4) \) and \( (x_2, y_2) = (3, -6) \).

Plugging in the coordinates into the formula:

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = 3 - (-7) = 3 + 7 = 10
\]

2. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = -6 - (-4) = -6 + 4 = -2
\]

3. Substitute into the distance formula:
\[
d = \sqrt{{(10)}^2 + {(-2)}^2}
\]
\[
d = \sqrt{100 + 4} = \sqrt{104}
\]

4. Calculate \(\sqrt{104}\):
\[
\sqrt{104} \approx 10.198 \quad (\text{using a calculator})
\]

Now rounding to the nearest tenth:
\[
10.198 \approx 10.2
\]

Therefore, the distance between the two points is approximately \(\boxed{10.2}\).