the midpoint M of PQ has coordinates -18,45. Point P has coordinates 55,-68 find the coordinates of point Q

To find the coordinates of point \( Q \), we can use the midpoint formula:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Where:
- \( M \) is the midpoint,
- \( P(x_1, y_1) \) is one endpoint, and
- \( Q(x_2, y_2) \) is the other endpoint.

Given:
- The midpoint \( M = (-18, 45) \),
- Point \( P = (55, -68) \).

Let \( Q = (x_2, y_2) \).

### Step 1: Solve for \( x_2 \)
Using the x-coordinate of the midpoint:

\[
\frac{55 + x_2}{2} = -18
\]

Multiply both sides by 2:

\[
55 + x_2 = -36
\]

Solve for \( x_2 \):

\[
x_2 = -36 - 55 = -91
\]

### Step 2: Solve for \( y_2 \)
Using the y-coordinate of the midpoint:

\[
\frac{-68 + y_2}{2} = 45
\]

Multiply both sides by 2:

\[
-68 + y_2 = 90
\]

Solve for \( y_2 \):

\[
y_2 = 90 + 68 = 158
\]

### Conclusion:
The coordinates of point \( Q \) are \( (-91, 158) \).

Would you like further clarification or details?

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Here are 5 related questions to explore:
1. How do you find the distance between two points?
2. What is the formula for the slope of a line?
3. How can you verify that a point is the midpoint of a line segment?
4. How do you find the equation of a line given two points?
5. How do you find the centroid of a triangle?

**Tip:** Always double-check midpoint calculations by plugging your results back into the midpoint formula.

The midpoint M of PQ has coordinates -18, 45. Point P has coordinates 55, -68. Find the coordinates of point Q.

Learn how to find the coordinates of point Q when given the midpoint M(-18, 45) and point P(55, -68). This problem explores the midpoint formula in coordinate geometry and is suitable for students in Grades 8-10.

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