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

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

We are given that $M(9, 8)$ is the midpoint of segment $RS$, and the coordinates of $S$ are $(10, 10)$. Let the coordinates of $R$ be $(x_1, y_1)$. Using the midpoint formula:

$(9, 8) = \left( \frac{x_1 + 10}{2}, \frac{y_1 + 10}{2} \right)$

We can set up two separate equations for the $x$-coordinates and $y$-coordinates:

1. For the $x$-coordinate: $\frac{x_1 + 10}{2} = 9$ Multiplying both sides by 2: $x_1 + 10 = 18$ Solving for $x_1$: $x_1 = 18 - 10 = 8$

2. For the $y$-coordinate: $\frac{y_1 + 10}{2} = 8$ Multiplying both sides by 2: $y_1 + 10 = 16$ Solving for $y_1$: $y_1 = 16 - 10 = 6$

Thus, the coordinates of $R$ are $(8, 6)$.

Answer:

a. (8, 6)

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Would you like a more detailed explanation or help with any other problems?

Here are 5 related questions to explore:

1. How do you calculate the midpoint of two points in a 3D coordinate system?
2. What is the distance formula between two points, and how does it relate to the midpoint?
3. How can you find the equation of a line given the midpoint and one endpoint?
4. If the midpoint is given, how do you find the slope of the line segment?
5. How would you use the midpoint formula to solve problems involving geometric figures like triangles or quadrilaterals?

Tip: Remember that the midpoint formula works for both the x- and y-coordinates independently!