A triangle has vertices on a coordinate grid at F, of, 7, comma, minus, 1F(7,−1), G, of, minus, 8, comma, minus, 1G(−8,−1), and H, of, 7, comma, 6, .H(7,6). What is the length, in units, of start overline, F, G, end overline 
FG
 ?

The length of a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a coordinate grid is calculated using the distance formula:

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

For the points \( F(7, -1) \) and \( G(-8, -1) \), the coordinates are as follows:
- \( F(7, -1) \)
- \( G(-8, -1) \)

Now, applying the distance formula:

\[
d = \sqrt{(-8 - 7)^2 + (-1 - (-1))^2}
\]
\[
d = \sqrt{(-15)^2 + (0)^2}
\]
\[
d = \sqrt{225}
\]
\[
d = 15
\]

Therefore, the length of the line segment \( \overline{FG} \) is **15 units**.

Would you like any further details or clarifications?

Here are 5 related questions:
1. What is the distance between points \( G(-8, -1) \) and \( H(7, 6) \)?
2. What is the perimeter of triangle \( FGH \)?
3. How do you calculate the midpoint of a line segment?
4. Can you calculate the slope of the line segment \( FG \)?
5. How do you find the area of triangle \( FGH \) using the coordinate points?

**Tip:** When calculating the distance between points on the same horizontal or vertical line, the formula simplifies to just the difference between the \(x\)-coordinates or \(y\)-coordinates!

A triangle has vertices on a coordinate grid at F(7,−1), G(−8,−1), and H(7,6). What is the length, in units, of the line segment FG?

Learn how to calculate the distance between two points, F(7,-1) and G(-8,-1), using the distance formula. This problem covers key geometry concepts such as coordinate geometry and the Pythagorean theorem. Suitable for students in Grades 8-10.

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