Question

Find the distance between the two points rounding to the nearest tenth
(3,6) and (-1,8)

Answer 1

To find the distance between the two points \((3, 6)\) and \((-1, 8)\), we can use the distance formula:

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

Where \((x_1, y_1) = (3, 6)\) and \((x_2, y_2) = (-1, 8)\).

Now, substituting the coordinates into the formula:

\[
d = \sqrt{((-1) - 3)^2 + (8 - 6)^2}
\]

Calculating inside the parentheses:

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

Calculating the squares:

\[
d = \sqrt{16 + 4}
\]

Adding the results:

\[
d = \sqrt{20}
\]

Now, simplifying \(\sqrt{20}\):

\[
d = \sqrt{4 \times 5} = 2\sqrt{5}
\]

Using a calculator to approximate \( \sqrt{5} \approx 2.236\):

\[
d \approx 2 \times 2.236 = 4.472
\]

Rounding to the nearest tenth:

\[
d \approx 4.5
\]

Thus, the distance between the points \((3,6)\) and \((-1,8)\) is approximately **4.5**.