To find the coordinates of $B$, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint $M$ of a line segment with endpoints $A(x_1, y_1)$ and $B(x_2, y_2)$ are given by:

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

Given:

• Midpoint $M(-2, 4)$
• Coordinates of $A(-1, 6)$
• Coordinates of $B(x_2, y_2)$ are unknown.

Step 1: Write midpoint equations

$-2 = \frac{-1 + x_2}{2} \quad \text{(for the x-coordinate)}$ $4 = \frac{6 + y_2}{2} \quad \text{(for the y-coordinate)}$

Step 2: Solve for $x_2$

Multiply both sides of the x-coordinate equation by 2: $-4 = -1 + x_2$ $x_2 = -4 + 1 = -3$

Step 3: Solve for $y_2$

Multiply both sides of the y-coordinate equation by 2: $8 = 6 + y_2$ $y_2 = 8 - 6 = 2$

Final Answer:

The coordinates of $B$ are: $B(-3, 2)$

Let me know if you'd like a detailed breakdown or have further questions! 😊

Relative Questions:

1. How do you verify the midpoint of a line segment?
2. What are some applications of the midpoint formula in geometry?
3. Can the midpoint formula be extended to three dimensions? How?
4. What if $A$ and $B$ were both variables? How would you solve for the midpoint?
5. How can you use the midpoint formula to find the equation of the perpendicular bisector?

Tip:

Always double-check your arithmetic when solving midpoint problems to avoid errors in simple addition or subtraction.