To solve this problem, we need to find the coordinates of the endpoint $S$ when given:

1. The midpoint $M(8, 6)$.
2. One endpoint $R(6, 10)$.

We can use the midpoint formula, which states that if $M(x_m, y_m)$ is the midpoint of points $R(x_1, y_1)$ and $S(x_2, y_2)$, then:

$x_m = \frac{x_1 + x_2}{2} \quad \text{and} \quad y_m = \frac{y_1 + y_2}{2}$

Given:

• $x_m = 8$ and $y_m = 6$
• $x_1 = 6$ and $y_1 = 10$

We can set up equations to solve for $x_2$ and $y_2$:

1. For the x-coordinate: $8 = \frac{6 + x_2}{2}$ Multiply both sides by 2: $16 = 6 + x_2$ Subtract 6 from both sides: $x_2 = 10$

2. For the y-coordinate: $6 = \frac{10 + y_2}{2}$ Multiply both sides by 2: $12 = 10 + y_2$ Subtract 10 from both sides: $y_2 = 2$

Thus, the coordinates of the other endpoint $S$ are $(10, 2)$.

Would you like a detailed explanation of each step or have any further questions?

Here are some related questions to explore:

1. How do you find the midpoint between two points given their coordinates?
2. What if both endpoints are unknown, and only the midpoint and distance are given?
3. How can the midpoint formula be used in three-dimensional space?
4. If the midpoint formula is rearranged, can it be used to find a point that divides a line segment in a given ratio?
5. How does the distance formula relate to the midpoint formula in coordinate geometry?

Tip: To double-check your answer, plug the coordinates of $R$ and $S$ into the midpoint formula to ensure they result in $M$.