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.