Question

Find the distance between point
A
(
−
5
,

7
)
A(−5, 7) and
B
(
7
,

11
)
B(7, 11). 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 \( A(-5, 7) \) and \( B(7, 11) \), you can use the distance formula:

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

where
- \( (x_1, y_1) \) are the coordinates of point A, and
- \( (x_2, y_2) \) are the coordinates of point B.

Substituting the coordinates of points A and B into the formula:

1. Identify the coordinates:
- \( x_1 = -5 \), \( y_1 = 7 \)
- \( x_2 = 7 \), \( y_2 = 11 \)

2. Plug in the values:
\[
d = \sqrt{(7 - (-5))^2 + (11 - 7)^2}
\]

3. Simplify:
\[
= \sqrt{(7 + 5)^2 + (11 - 7)^2}
\]
\[
= \sqrt{(12)^2 + (4)^2}
\]
\[
= \sqrt{144 + 16}
\]
\[
= \sqrt{160}
\]

4. Now calculate \( \sqrt{160} \):
\[
\sqrt{160} \approx 12.649
\]

5. Round to the nearest tenth:
\[
\approx 12.6
\]

So, the distance between points \( A(-5, 7) \) and \( B(7, 11) \) is approximately **12.6**.