The midpoint of JK is M. Find the coordinates of the missing endpoint if (2,7) and M(-4,3)

We can find the coordinates of the missing endpoint using the midpoint formula.

The formula for the midpoint \( M \) of a line segment with endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \) is:

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

In this case, we know:
- One endpoint \( J = (2, 7) \)
- The midpoint \( M = (-4, 3) \)
- We need to find the coordinates of the other endpoint \( K = (x_2, y_2) \).

Let's break it down step by step.

### Step 1: Set up the midpoint equations
From the midpoint formula, we can set up two equations, one for the x-coordinates and one for the y-coordinates:

\[
\frac{2 + x_2}{2} = -4 \quad \text{(for the x-coordinate)}
\]
\[
\frac{7 + y_2}{2} = 3 \quad \text{(for the y-coordinate)}
\]

### Step 2: Solve for \( x_2 \)
\[
\frac{2 + x_2}{2} = -4
\]
Multiply both sides by 2:
\[
2 + x_2 = -8
\]
Subtract 2 from both sides:
\[
x_2 = -10
\]

### Step 3: Solve for \( y_2 \)
\[
\frac{7 + y_2}{2} = 3
\]
Multiply both sides by 2:
\[
7 + y_2 = 6
\]
Subtract 7 from both sides:
\[
y_2 = -1
\]

### Final Answer:
The coordinates of the missing endpoint \( K \) are \( (-10, -1) \).

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Would you like a detailed explanation of the process? 

Here are 5 related questions for practice:
1. Find the missing endpoint if the midpoint is \( (3, 5) \) and one endpoint is \( (7, 2) \).
2. What is the formula for finding the distance between two points?
3. If the midpoint of a line is \( (0, 0) \), and one endpoint is \( (4, 6) \), what is the other endpoint?
4. Find the midpoint of the line segment with endpoints \( (1, 2) \) and \( (-5, 4) \).
5. If the midpoint is \( (-2, 7) \), and one endpoint is \( (-5, 3) \), what is the missing endpoint?

**Tip:** When finding missing endpoints, always solve the x and y coordinates separately to avoid confusion.

Discover how to find the missing endpoint of a line segment when given one endpoint (2,7) and the midpoint M(-4,3). Using the midpoint formula, we provide a step-by-step solution suitable for students in Grades 6-8.

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