To find the coordinates of point $Q(x_1, y_1)$, we can use the midpoint formula. The midpoint $M$ of a line segment with endpoints $Q(x_1, y_1)$ and $R(x_2, y_2)$ is given by:

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

Given:

• Midpoint $M = (-17.5, -1)$
• Point $R = (-18, -10)$

We need to find $Q(x_1, y_1)$.

Using the midpoint formula:

$-17.5 = \frac{x_1 + (-18)}{2}$ $-1 = \frac{y_1 + (-10)}{2}$

Solving for $x_1$:

$-17.5 = \frac{x_1 - 18}{2}$ Multiply both sides by 2: $-35 = x_1 - 18$ Add 18 to both sides: $x_1 = -35 + 18 = -17$

Solving for $y_1$:

$-1 = \frac{y_1 - 10}{2}$ Multiply both sides by 2: $-2 = y_1 - 10$ Add 10 to both sides: $y_1 = -2 + 10 = 8$

So, the coordinates of point $Q$ are $\boxed{(-17, 8)}$.

Would you like more details or have any questions?
Here are five related questions to consider:

1. How do you find the distance between two points?
2. What is the formula for finding the slope of a line segment?
3. How do you find the equation of a line given two points?
4. What are the coordinates of a point if the midpoint and one endpoint are given as variables?
5. How can you verify if a given point lies on a line segment?

Tip: Always verify your calculations by substituting back into the original formula.