Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)
midpoint ​(negative 10​,15​), endpoint ​(negative 9​,18​)
Question content area bottom
Part 1
The other endpoint is 
  
enter your response here.


To find the coordinates of the other endpoint, let's denote the unknown endpoint as \((x, y)\). 

Given:
- Midpoint \((x_m, y_m) = (-10, 15)\)
- Known endpoint \((x_1, y_1) = (-9, 18)\)

The midpoint formula is given by:
\[
\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = (x_m, y_m)
\]

Using this formula, we can set up the following equations:
\[
\frac{-9 + x}{2} = -10
\]
\[
\frac{18 + y}{2} = 15
\]

Now, solve each equation for \(x\) and \(y\):

### Solving for \(x\):
\[
\frac{-9 + x}{2} = -10
\]
Multiply both sides by 2:
\[
-9 + x = -20
\]
Add 9 to both sides:
\[
x = -11
\]

### Solving for \(y\):
\[
\frac{18 + y}{2} = 15
\]
Multiply both sides by 2:
\[
18 + y = 30
\]
Subtract 18 from both sides:
\[
y = 12
\]

Thus, the coordinates of the other endpoint are \((-11, 12)\).

Would you like more details on how these calculations were done, or do you have any other questions?

Here are some related questions you might find interesting:
1. How do you derive the midpoint formula?
2. Can you find the distance between the two endpoints using their coordinates?
3. How would the midpoint formula change in three-dimensional space?
4. What are some real-world applications of finding midpoints?
5. How can you verify that \((-11, 12)\) is indeed the correct endpoint?

**Tip:** When solving midpoint problems, always double-check your equations by plugging the coordinates back into the midpoint formula.

Learn how to find the coordinates of an endpoint using the midpoint formula with a detailed step-by-step solution. This problem covers coordinate geometry concepts and the application of the midpoint formula to determine unknown endpoints. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation