Question

What is the length of segment GH?

On a coordinate plane, line G H has points (0, negative 3), (8, 1).
StartRoot 48 EndRoot units
8 units
StartRoot 80 EndRoot units
12 units

Answer 1

To find the length of segment \( GH \) given the points \( G(0, -3) \) and \( H(8, 1) \), we can use the distance formula, which is defined as:

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

In this case, \( (x_1, y_1) = (0, -3) \) and \( (x_2, y_2) = (8, 1) \). Plugging these values into the formula gives us:

\[
d = \sqrt{(8 - 0)^2 + (1 - (-3))^2}
\]

Calculating inside the parentheses first:

\[
= \sqrt{(8)^2 + (1 + 3)^2}
\]
\[
= \sqrt{64 + 4^2}
\]
\[
= \sqrt{64 + 16}
\]
\[
= \sqrt{80}
\]

Thus, the length of segment \( GH \) is:

\[
\sqrt{80} \text{ units}
\]

This can be simplified further:

\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}
\]

Since this corresponds with the options given:

- \( \sqrt{48} \) (not a match)
- \( 8 \) (not a match)
- \( \sqrt{80} \) (a match)
- \( 12 \) (not a match)

The answer is:

\[
\sqrt{80} \text{ units}
\]