Question

Find the distance between point
𝐴
(
−
3
,

10
)
A(−3, 10) and
𝐵
(
6
,

−
7
)
B(6, −7). Round your answer to the nearest tenth.

Answer 1

To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we can use the distance formula:

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

In this case, the coordinates of the points are:
- \( A(-3, 10) \) which gives \( x_1 = -3 \) and \( y_1 = 10 \)
- \( B(6, -7) \) which gives \( x_2 = 6 \) and \( y_2 = -7 \)

Now, we can plug in these values into the formula:

\[
d = \sqrt{(6 - (-3))^2 + (-7 - 10)^2}
\]

Calculating the differences:

\[
6 - (-3) = 6 + 3 = 9 \quad \text{and} \quad -7 - 10 = -17
\]

Now substitute these differences back into the formula:

\[
d = \sqrt{(9)^2 + (-17)^2}
\]

Calculating the squares:

\[
d = \sqrt{81 + 289}
\]

Adding them together:

\[
d = \sqrt{370}
\]

Using a calculator to find the square root of \( 370 \):

\[
d \approx 19.2
\]

Rounding to the nearest tenth, the distance between points \( A \) and \( B \) is:

\[
\boxed{19.2}
\]