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

15.8 units
15.8 units

16.2 units
16.2 units

10.0 units
10.0 units

20.0 units

Answer 1

To find the distance between the points (6, 1) and (−9, 6) in the coordinate plane, we can use the distance formula:

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

Here, the coordinates are:
- \( (x_1, y_1) = (6, 1) \)
- \( (x_2, y_2) = (-9, 6) \)

Now, substituting the values into the formula:

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

To simplify \(\sqrt{250}\):

\[
\sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5\sqrt{10}
\]

Now, we calculate \(5\sqrt{10}\) using an approximation for \(\sqrt{10}\):

\(\sqrt{10} \approx 3.1623\)

Thus,

\[
5\sqrt{10} \approx 5 \times 3.1623 \approx 15.8115
\]

Rounding this to the nearest tenth, we get:

\[
15.8
\]

Therefore, the distance between the points (6,1) and (−9,6) is approximately **15.8 units**.