To find the other endpoint of a line segment when one endpoint and the midpoint are given, you can use the midpoint formula. The midpoint \((M_x, M_y)\) of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
M_x = \frac{x_1 + x_2}{2}, \quad M_y = \frac{y_1 + y_2}{2}
\]

Given:
- One endpoint: \((-5, 5)\)
- Midpoint: \((7, 3)\)

Let the other endpoint be \((x_2, y_2)\).

Using the midpoint formula:

\[
7 = \frac{-5 + x_2}{2}
\]
\[
3 = \frac{5 + y_2}{2}
\]

Now, solve these equations:

1. For the \(x\)-coordinate:
\[
7 = \frac{-5 + x_2}{2}
\]
Multiply both sides by 2:
\[
14 = -5 + x_2
\]
Add 5 to both sides:
\[
x_2 = 19
\]

2. For the \(y\)-coordinate:
\[
3 = \frac{5 + y_2}{2}
\]
Multiply both sides by 2:
\[
6 = 5 + y_2
\]
Subtract 5 from both sides:
\[
y_2 = 1
\]

So, the other endpoint is \((19, 1)\).

Would you like more details or have any questions?

Here are some related questions:

1. How do you derive the midpoint formula?
2. What is the significance of the midpoint in geometry?
3. Can the midpoint formula be extended to three dimensions?
4. How would you find the length of the line segment between two points?
5. What is the distance formula between two

Learn how to find the endpoint of a line segment given one endpoint and the midpoint using the midpoint formula. This problem involves coordinate geometry and requires understanding of the midpoint formula. Suitable for Grades 9-12 students.

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