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To determine the correct expression that represents the distance between points \( G(-9, -12) \) and \( H(-9, 6) \), we can use the following approach:

Since both points share the same \( x \)-coordinate (\( -9 \)), they lie on the same vertical line. The distance between them will be the difference in their \( y \)-coordinates, which are \( -12 \) and \( 6 \).

1. The distance formula for points on the same vertical line is the absolute difference of their \( y \)-coordinates:
\[
\text{Distance} = |y_2 - y_1| = |6 - (-12)| = |6 + 12| = |18| = 18
\]
So, the correct expression involves the absolute difference of the \( y \)-coordinates.

Among the options:
- \( |-12| + |6| \)
- \( |-12| + |-9| \)
- \( |-12| - |6| \)
- \( |-9| - |-6| \)

The correct expression is \( |-12| + |6| \), which corresponds to the absolute values of the two \( y \)-coordinates being added.

Let me know if you'd like more details or have any questions. 

Here are 5 related questions to consider:
1. How would you calculate the distance if the points had different \( x \)-coordinates as well?
2. What is the formula for calculating the Euclidean distance between two arbitrary points?
3. What would be the result if we were to calculate the horizontal distance between points with the same \( y \)-coordinates?
4. How can we visualize the absolute value function in geometry?
5. What is the significance of absolute values when determining distance in coordinate geometry?

**Tip**: When calculating distances on a coordinate plane, always consider the differences in both \( x \)-coordinates and \( y \)-coordinates. If only one coordinate changes, the distance is the absolute difference of the changing coordinate.

Which expression represents the distance between point G and point H?

Learn how to calculate the distance between two points G(-9, -12) and H(-9, 6) that lie on the same vertical line in the coordinate plane. This problem involves using absolute value and distance formulas, ideal for students in Grades 6-8.

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