To find the other endpoint of a line segment when one endpoint and the midpoint are given, you can use the midpoint formula:

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

Given:

• One endpoint: $(-5, 5)$
• Midpoint: $(7, 3)$

Let's call the other endpoint $(x, y)$.

Using the midpoint formula:

$\left( \frac{-5 + x}{2}, \frac{5 + y}{2} \right) = (7, 3)$

This gives us two equations:

$\frac{-5 + x}{2} = 7 \quad \text{and} \quad \frac{5 + y}{2} = 3$

Let's solve these:

1. Solve for $x$:

$\frac{-5 + x}{2} = 7$

Multiply both sides by 2:

$-5 + x = 14$

Add 5 to both sides:

$x = 19$

2. Solve for $y$:

$\frac{5 + y}{2} = 3$

Multiply both sides by 2:

$5 + y = 6$

Subtract 5 from both sides:

$y = 1$

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

Would you like more details or have any other questions?

Related Questions:

1. How do you calculate the distance between two points?
2. What is the formula for finding the slope of a line?
3. How can you find the equation of a line given two points?
4. What is the significance of the midpoint in geometry?
5. How do you find the centroid of a triangle given its vertices?
6. What is the formula for the area of a triangle given three points?
7. How do you reflect a point across a line?
8. What is the equation of a circle given its center and a point on the circle?

Tip: When working with line segments, always remember the midpoint formula as it is key for finding missing points.