Question

Lulu marks the points (1, 7) and (6, 2) on the coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?(1 point) Responses 6.2 units 6.2 units 10.3 units 10.3 units 7.1 units 7.1 units 7.8 units

Answer 1

To find the distance between the points \((1, 7)\) and \((6, 2)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (1, 7)\) and \((x_2, y_2) = (6, 2)\).

Now, substitute the coordinates into the formula:

\[
d = \sqrt{(6 - 1)^2 + (2 - 7)^2}
\]

Calculating the differences:

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

Calculating the squares:

\[
d = \sqrt{25 + 25}
\]

\[
d = \sqrt{50}
\]

To express \(\sqrt{50}\), we can simplify it:

\[
\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}
\]

Now, we can approximate \(\sqrt{2} \approx 1.414\):

\[
d \approx 5 \cdot 1.414 \approx 7.07
\]

Now rounding to the nearest tenth:

\[
d \approx 7.1
\]

So, the distance between the two points is approximately **7.1 units**.