Question

What is the length of the line segment between point A and point B? Use square root notation to write the exact value of the line segment. Solve on paper if you’d like, then enter your answer on Zearn.
A (-2,7)
B (5,-6)

Answer 1

To find the length of the line segment between point A \((-2, 7)\) and point B \((5, -6)\), we can use the distance formula, which is given by:

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

Where:
- \((x_1, y_1)\) are the coordinates of point A
- \((x_2, y_2)\) are the coordinates of point B

Substituting in the coordinates of points A and B:

\[
x_1 = -2, \quad y_1 = 7
\]
\[
x_2 = 5, \quad y_2 = -6
\]

Now, we can plug these values into the distance formula:

\[
d = \sqrt{(5 - (-2))^2 + (-6 - 7)^2}
\]

Calculating inside the parentheses:

\[
d = \sqrt{(5 + 2)^2 + (-6 - 7)^2}
\]
\[
d = \sqrt{(7)^2 + (-13)^2}
\]

Now, calculate the squares:

\[
d = \sqrt{49 + 169}
\]

Adding the results:

\[
d = \sqrt{218}
\]

Thus, the length of the line segment between points A and B is:

\[
\sqrt{218}
\]

This is the exact value of the line segment.