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 $(-10, -1)$.

---

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.