find the coordinates of the other endpoint of the segment with the given endpoints and midpoint M. R(7,-17) M(-2,3)

To find the coordinates of the other endpoint of a line segment when one endpoint and the midpoint are given, we can use the midpoint formula.

The midpoint \(M\) of a line segment with endpoints \(A(x_1, y_1)\) and \(B(x_2, y_2)\) is given by:

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

Given:
- Endpoint \(R(7, -17)\)
- Midpoint \(M(-2, 3)\)

Let \(R(7, -17)\) be \((x_1, y_1)\) and let the other endpoint \(Q(x_2, y_2)\) be \((x_2, y_2)\). The midpoint formula becomes:

\[
(-2, 3) = \left( \frac{7 + x_2}{2}, \frac{-17 + y_2}{2} \right)
\]

We can set up equations for \(x_2\) and \(y_2\) by equating each coordinate:

1. \[
-2 = \frac{7 + x_2}{2}
\]

2. \[
3 = \frac{-17 + y_2}{2}
\]

Let's solve these equations for \(x_2\) and \(y_2\).The coordinates of the other endpoint \(Q\) are \((-11, 23)\).

### Summary:
- Given endpoint \(R(7, -17)\)
- Midpoint \(M(-2, 3)\)
- The other endpoint \(Q\) is \((-11, 23)\).

Would you like more details or have any questions?

### Related Questions:
1. How do you derive the midpoint formula for a line segment?
2. How can we find the length of a segment given its endpoints?
3. What is the distance formula between two points in a coordinate plane?
4. How to find the slope of a line passing through two points?
5. How can you find the equation of a line given a point and its slope?

**Tip:** Always verify your results by substituting them back into the original formula to check for consistency.

Find the coordinates of the other endpoint of the segment with the given endpoints and midpoint M. R(7,-17) M(-2,3)

Learn how to find the coordinates of the other endpoint of a line segment when given one endpoint R(7, -17) and the midpoint M(-2, 3). This problem involves applying the midpoint formula and solving linear equations. Suitable for students in Grades 8-10.

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