To find the coordinates of the other endpoint $S(x, y)$ of the segment $RS$ when given the endpoint $R(x_1, y_1)$ and the midpoint $M(x_m, y_m)$, you can use the midpoint formula:

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

Given:

• $R(x_1, y_1) = (7, -17)$
• $M(x_m, y_m) = (-2, 3)$

Let's denote the coordinates of the other endpoint $S$ as $(x_2, y_2)$.

Using the midpoint formula: $x_m = \frac{x_1 + x_2}{2} \quad \text{and} \quad y_m = \frac{y_1 + y_2}{2}$

Substitute the values for $x_m$, $y_m$, $x_1$, and $y_1$:

$-2 = \frac{7 + x_2}{2} \quad \text{and} \quad 3 = \frac{-17 + y_2}{2}$

Now, solve for $x_2$ and $y_2$:

Solve for $x_2$:

$-2 = \frac{7 + x_2}{2}$ Multiply both sides by 2: $-4 = 7 + x_2$ Subtract 7 from both sides: $x_2 = -11$

Solve for $y_2$:

$3 = \frac{-17 + y_2}{2}$ Multiply both sides by 2: $6 = -17 + y_2$ Add 17 to both sides: $y_2 = 23$

Therefore, the coordinates of the other endpoint $S$ are $\boxed{(-11, 23)}$.

Would you like to explore any further details or have any other questions?

Here are 5 related questions:

1. How would you find the distance between the endpoints $R$ and $S$?
2. What is the equation of the line passing through points $R$ and $S$?
3. How do you determine if two segments are perpendicular given their endpoints?
4. Can you verify that the calculated point $S$ is correct using the midpoint formula?
5. What would be the coordinates of the midpoint if the endpoints were swapped?

Tip: Always check your final answer by substituting it back into the original equation to ensure accuracy.