The coordinates of the midpoint of GHare M (-2, 5) and the coordinates of one endpoint are H (-3, 7).

To find the coordinates of the other endpoint \( G(x, y) \) of the line segment GH, given that the midpoint \( M(-2, 5) \) and one endpoint \( H(-3, 7) \) are known, we can use the midpoint formula.

### Midpoint Formula
The midpoint \( M \) of a line segment with endpoints \( G(x_1, y_1) \) and \( H(x_2, y_2) \) is given by:
\[
M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]
Substituting \( M(-2, 5) \), \( H(-3, 7) \), and \( G(x, y) \) into the formula:
\[
\left(\frac{-3 + x}{2}, \frac{7 + y}{2}\right) = (-2, 5)
\]

### Solve for \( x \) and \( y \):
- For the x-coordinate:
\[
\frac{-3 + x}{2} = -2
\]
Multiply both sides by 2:
\[
-3 + x = -4
\]
Add 3 to both sides:
\[
x = -1
\]

- For the y-coordinate:
\[
\frac{7 + y}{2} = 5
\]
Multiply both sides by 2:
\[
7 + y = 10
\]
Subtract 7 from both sides:
\[
y = 3
\]

### Coordinates of Point G
The coordinates of the other endpoint \( G \) are \( (-1, 3) \).

Would you like any further details or have any questions?

Here are some related questions:
1. How do you find the distance between points G and H?
2. What is the equation of the line passing through G and H?
3. How do you find the slope of GH using these coordinates?
4. What would be the coordinates if you reflected point G across the x-axis?
5. How do you determine the midpoint if you know both endpoints?

**Tip:** When given a midpoint and one endpoint, you can always find the other endpoint by setting up and solving the midpoint formula equations as we did above.

Learn how to find the coordinates of point G using the midpoint formula in coordinate geometry. Given midpoint M(-2, 5) and endpoint H(-3, 7), discover the step-by-step process to determine the coordinates of point G. Suitable for students in Grades 9-10.

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