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 15​,8​), endpoint ​(negative 6​,12​)

To find the coordinates of the other endpoint of a segment, given its midpoint and one endpoint, we use the midpoint formula:

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

Where \((x_1, y_1)\) are the coordinates of the known endpoint, \((x_2, y_2)\) are the coordinates of the unknown endpoint, and the midpoint is given as \((M_x, M_y)\).

### Given:
- Midpoint: \((-15, 8)\)
- Known Endpoint: \((-6, 12)\)
- Let the unknown endpoint be \((x, y)\).

### Step 1: Apply the midpoint formula

We know the midpoint formula gives us the following two equations based on the \(x\)- and \(y\)-coordinates:

\[
\frac{-6 + x}{2} = -15
\]
\[
\frac{12 + y}{2} = 8
\]

### Step 2: Solve for \(x\) and \(y\)

1. Solve for \(x\):

\[
\frac{-6 + x}{2} = -15
\]

Multiply both sides by 2:

\[
-6 + x = -30
\]

Now, solve for \(x\):

\[
x = -30 + 6 = -24
\]

2. Solve for \(y\):

\[
\frac{12 + y}{2} = 8
\]

Multiply both sides by 2:

\[
12 + y = 16
\]

Now, solve for \(y\):

\[
y = 16 - 12 = 4
\]

### Conclusion:
The coordinates of the other endpoint are \((-24, 4)\).

Would you like more details or have any further questions?

Here are some related questions to explore:
1. How do you derive the midpoint formula?
2. What are other applications of the midpoint formula?
3. How do you find the distance between two points?
4. What is the slope of a line given two points?
5. How can you use vectors to solve this problem?

**Tip:** Always ensure to double-check your algebraic steps when solving midpoint-related problems to avoid simple errors.

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. Midpoint (-15, 8), endpoint (-6, 12).

Discover how to find the coordinates of the other endpoint of a segment when given its midpoint (-15, 8) and one endpoint (-6, 12). This solution uses the midpoint formula and linear equations to provide a step-by-step approach. Suitable for students in Grades 7-10.

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