Question

Beth Anne marks the points (6,1)
and (−9,6)
on the coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?(1 point)
Responses

16.2 units
16.2 units

15.8 units
15.8 units

20.0 units
20.0 units

10.0 units
10.0 units

Answer 1

To find the distance between the points \( (6,1) \) and \( (-9,6) \), we can use the distance formula, which is given by:

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

Here, \( (x_1, y_1) = (6, 1) \) and \( (x_2, y_2) = (-9, 6) \).

Substituting the values into the formula:

\[
d = \sqrt{((-9) - 6)^2 + (6 - 1)^2}
\]
\[
= \sqrt{(-15)^2 + (5)^2}
\]
\[
= \sqrt{225 + 25}
\]
\[
= \sqrt{250}
\]
\[
= \sqrt{25 \times 10}
\]
\[
= 5\sqrt{10}
\]

Next, we calculate \( 5\sqrt{10} \). Using an approximate value for \( \sqrt{10} \approx 3.162 \):

\[
5\sqrt{10} \approx 5 \times 3.162 \approx 15.81
\]

Rounding this to the nearest tenth gives us approximately \( 15.8 \) units.

Thus, the distance between the two points, rounded to the nearest tenth of a unit, is:

**15.8 units**