Question

Find the distance between point
A
(
−
3
,

5
)
A(−3, 5) and
B
(
4
,

14
)
B(4, 14). Round your answer to the nearest tenth. Even an answer like 15 should be written as 15.0.

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Answer 1

To find the distance between the points \( A(-3, 5) \) and \( B(4, 14) \), we can use the distance formula:

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

Where:
- \( (x_1, y_1) = (-3, 5) \)
- \( (x_2, y_2) = (4, 14) \)

Now, substitute the coordinates into the formula:

1. Calculate \( x_2 - x_1 \):
\[
4 - (-3) = 4 + 3 = 7
\]

2. Calculate \( y_2 - y_1 \):
\[
14 - 5 = 9
\]

Now, plug these values into the distance formula:

\[
d = \sqrt{(7)^2 + (9)^2}
\]

3. Calculate \( (7)^2 \) and \( (9)^2 \):
\[
7^2 = 49
\]
\[
9^2 = 81
\]

4. Now sum these values:
\[
49 + 81 = 130
\]

5. Take the square root:
\[
d = \sqrt{130} \approx 11.401754
\]

Finally, round this to the nearest tenth:

\[
d \approx 11.4
\]

Thus, the distance between points \( A(-3, 5) \) and \( B(4, 14) \) is approximately \( \boxed{11.4} \).