Question

Find the distance between the points (8,4) and (1,10). Round decimals to the nearest tenth.

Answer 1

To find the distance between the points (8, 4) and (1, 10), we can use the distance formula:

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

Where:
- \((x_1, y_1) = (8, 4)\)
- \((x_2, y_2) = (1, 10)\)

Substituting the values into the formula:

\[
d = \sqrt{(1 - 8)^2 + (10 - 4)^2}
\]
\[
d = \sqrt{(-7)^2 + (6)^2}
\]
\[
d = \sqrt{49 + 36}
\]
\[
d = \sqrt{85}
\]

Now, we will calculate \(\sqrt{85}\).

\[
\sqrt{85} \approx 9.219544
\]

Rounding to the nearest tenth:

\[
d \approx 9.2
\]

Thus, the distance between the points (8, 4) and (1, 10) is approximately **9.2**.