Question

What is the length of segment RS?
On a coordinate plane, line R S has points (negative 4, negative 3) and (1, 9).
StartRoot 65 EndRoot
12
13
StartRoot 153 EndRoot

Answer 1

To find the length of segment RS with endpoints R(-4, -3) and S(1, 9), we can use the distance formula:

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

Here, \((x_1, y_1) = (-4, -3)\) and \((x_2, y_2) = (1, 9)\).

Now, substituting the coordinates into the formula:

\[
d = \sqrt{(1 - (-4))^2 + (9 - (-3))^2}
\]

Calculating the differences:

\[
d = \sqrt{(1 + 4)^2 + (9 + 3)^2}
\]
\[
d = \sqrt{(5)^2 + (12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

Thus, the length of segment RS is \(13\).