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The problem gives the midpoint \( M \) of line segment \( PQ \) at coordinates \( (-5, 2) \), and point \( P \) at coordinates \( (-7, -2) \). You are asked to find the coordinates of point \( Q \).

### Midpoint Formula:
The midpoint \( M \) of a line segment is given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points \( P \) and \( Q \), respectively.

### Step-by-step solution:
Let the coordinates of point \( Q \) be \( (x_2, y_2) \).

1. For the \( x \)-coordinates:
   \[
   -5 = \frac{-7 + x_2}{2}
   \]
   Multiply both sides by 2:
   \[
   -10 = -7 + x_2
   \]
   Add 7 to both sides:
   \[
   x_2 = -3
   \]

2. For the \( y \)-coordinates:
   \[
   2 = \frac{-2 + y_2}{2}
   \]
   Multiply both sides by 2:
   \[
   4 = -2 + y_2
   \]
   Add 2 to both sides:
   \[
   y_2 = 6
   \]

Thus, the coordinates of point \( Q \) are \( (-3, 6) \).

The correct answer is the last option: \( (-3, 6) \).

Would you like a more detailed explanation or have any further questions?

### Related questions:
1. How do you find the midpoint of a line segment if both points are known?
2. What is the distance formula between two points in a coordinate plane?
3. How can you determine if three points are collinear using coordinates?
4. What are the properties of a line segment's midpoint in geometry?
5. How do you solve for one endpoint when the midpoint and the other endpoint are given?

### Tip:
Always verify your answer by substituting the calculated point back into the midpoint formula to ensure correctness.

The midpoint of line segment PQ is located at M(-5, 2). If point P is located at (-7, -2), what are the coordinates of point Q?

Solve for the coordinates of point Q when given the midpoint M(-5, 2) and point P(-7, -2) using the midpoint formula. Learn how to calculate coordinates step by step. Suitable for students in Grades 7-10.

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