Question

The coordinates of the endpoint of line AB are A(-4,3) and B(1,-3). Which measurement is closest to the length of line AB in units?

8.4 units
6.8 units
7.4 units
7.8 units

Answer 1

To find the length of line segment AB with endpoints A(-4, 3) and B(1, -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 and \( (x_2, y_2) \) are the coordinates of point B.

Plugging in the coordinates:

- \( x_1 = -4 \), \( y_1 = 3 \)
- \( x_2 = 1 \), \( y_2 = -3 \)

Substituting these values into the distance formula:

\[
d = \sqrt{(1 - (-4))^2 + (-3 - 3)^2}
\]

This simplifies to:

\[
d = \sqrt{(1 + 4)^2 + (-3 - 3)^2}
\]
\[
d = \sqrt{(5)^2 + (-6)^2}
\]
\[
d = \sqrt{25 + 36}
\]
\[
d = \sqrt{61}
\]

Now, we can calculate \(\sqrt{61}\). It is approximately:

\[
\sqrt{61} \approx 7.81
\]

Among the provided options, the measurement closest to the length of line AB is:

**7.8 units.**