Question

Find the distance between point
A
(
4
,

7
)
A(4, 7) and
B
(
14
,

18
)
B(14, 18). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.

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:

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

Given the points:
- \( A(4, 7) \) where \( x_1 = 4 \) and \( y_1 = 7 \)
- \( B(14, 18) \) where \( x_2 = 14 \) and \( y_2 = 18 \)

Substituting the values into the distance formula:

\[
d = \sqrt{(14 - 4)^2 + (18 - 7)^2}
\]
\[
= \sqrt{(10)^2 + (11)^2}
\]
\[
= \sqrt{100 + 121}
\]
\[
= \sqrt{221}
\]

Calculating \( \sqrt{221} \):

\[
\sqrt{221} \approx 14.866
\]

Rounded to the nearest tenth, the distance \( d \) is approximately:

\[
\boxed{14.9}
\]