Question

The coordinates of points A and B are (–7, 5) and (4, –3), respectively. What is the distance, in units, between the points? Round to the nearest tenth if necessary.

Answer 1

To find the distance between points A \((-7, 5)\) and B \((4, -3)\), we 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,
- \((x_2, y_2)\) are the coordinates of point B.

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

\[
x_1 = -7, \quad y_1 = 5, \quad x_2 = 4, \quad y_2 = -3
\]

Now, we calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[
x_2 - x_1 = 4 - (-7) = 4 + 7 = 11
\]
\[
y_2 - y_1 = -3 - 5 = -8
\]

Next, we substitute these values into the distance formula:

\[
d = \sqrt{(11)^2 + (-8)^2}
\]
\[
d = \sqrt{121 + 64}
\]
\[
d = \sqrt{185}
\]

Calculating \(\sqrt{185}\):

\[
\sqrt{185} \approx 13.6
\]

Thus, the distance between points A and B is approximately \( \boxed{13.6} \) units.