The coordinates of the vertices of triangle GHI are G(0,3) , H(-8,7), and I(-5,9) what is the lenght of GH

To find the length of line segment \( GH \) between the points \( G(0, 3) \) and \( H(-8, 7) \), we can use the distance formula, which is given by:

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

For the points \( G(0, 3) \) and \( H(-8, 7) \), substitute \( x_1 = 0 \), \( y_1 = 3 \), \( x_2 = -8 \), and \( y_2 = 7 \) into the formula:

\[
d = \sqrt{(-8 - 0)^2 + (7 - 3)^2}
\]

\[
d = \sqrt{(-8)^2 + (4)^2}
\]

\[
d = \sqrt{64 + 16}
\]

\[
d = \sqrt{80}
\]

\[
d = 4\sqrt{5}
\]

The length of \( GH \) is \( 4\sqrt{5} \), or approximately 8.94 units.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would you find the length of the other sides, \( HI \) and \( GI \)?
2. What is the perimeter of triangle \( GHI \)?
3. How can you use these coordinates to find the area of triangle \( GHI \)?
4. What type of triangle is \( GHI \), based on its side lengths?
5. How do the slopes of the sides relate to the angles in triangle \( GHI \)?

**Tip**: Always double-check your arithmetic when using the distance formula!

The coordinates of the vertices of triangle GHI are G(0,3), H(-8,7), and I(-5,9). What is the length of GH?

Learn how to find the length of line segment GH in triangle GHI with coordinates G(0,3), H(-8,7) using the distance formula. This problem covers key geometry concepts and coordinate geometry. Suitable for students in Grades 8-10.

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