To find the coordinates of point B, we can use the midpoint formula, which states that the midpoint $M$ of a line segment between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by:

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

Given:

• Coordinates of $A$ are $(-3, 4)$.
• Midpoint $M$ is $(5, 0)$.

Let the coordinates of $B$ be $(x_2, y_2)$.

Step 1: Solve for $x_2$

$\frac{-3 + x_2}{2} = 5$ Multiply both sides by 2: $-3 + x_2 = 10$ Add 3 to both sides: $x_2 = 13$

Step 2: Solve for $y_2$

$\frac{4 + y_2}{2} = 0$ Multiply both sides by 2: $4 + y_2 = 0$ Subtract 4 from both sides: $y_2 = -4$

Thus, the coordinates of point B are $(13, -4)$.

The correct answer is: $\boxed{(13, -4)}$

Would you like a detailed explanation on how the midpoint formula works or have any other questions?

Related Questions:

1. How do you find the midpoint of a segment if both endpoints are given?
2. What is the distance formula between two points, and how is it used?
3. Can you determine a point that divides a segment in a specific ratio?
4. How do transformations like translations affect the coordinates of points?
5. How can the concept of midpoint be applied in three-dimensional geometry?

Tip:

Remember that to find one of the endpoints using the midpoint formula, you can rearrange the formula to solve for the unknown coordinate.