Question

The coordinates of the vertices of the triangle shown are F(1,9), G(5,6), and H(5,9).

What is length of segment FG in units?

Answer 1

To find the length of segment \( FG \) between the points \( F(1, 9) \) and \( G(5, 6) \), we can use the distance formula:

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

Substituting the coordinates of points \( F \) and \( G \) into the formula, we have:

- \( F(1, 9) \) implies \( x_1 = 1 \) and \( y_1 = 9 \)
- \( G(5, 6) \) implies \( x_2 = 5 \) and \( y_2 = 6 \)

Now, substituting these values into the distance formula:

\[
d = \sqrt{(5 - 1)^2 + (6 - 9)^2}
\]

Calculating each part:

- \( (5 - 1)^2 = 4^2 = 16 \)
- \( (6 - 9)^2 = (-3)^2 = 9 \)

Now plug these values back into the formula:

\[
d = \sqrt{16 + 9} = \sqrt{25}
\]

Finally, calculating the square root:

\[
d = 5
\]

Thus, the length of segment \( FG \) is \( \boxed{5} \) units.