To find the coordinates of point $B$, we can use the midpoint formula. The midpoint $M(x_m, y_m)$ of a line segment with endpoints $A(x_1, y_1)$ 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:

• $M(3, -4)$ is the midpoint.
• $A(7, -3)$ are the coordinates of point $A$.

We need to find the coordinates of point $B(x_2, y_2)$.

Solving for $x_2$:

The $x$-coordinate of the midpoint is given by:

$3 = \frac{7 + x_2}{2}$

Multiply both sides by 2:

$6 = 7 + x_2$

Subtract 7 from both sides:

$x_2 = -1$

Solving for $y_2$:

The $y$-coordinate of the midpoint is given by:

$-4 = \frac{-3 + y_2}{2}$

Multiply both sides by 2:

$-8 = -3 + y_2$

Add 3 to both sides:

$y_2 = -5$

Final Answer:

The coordinates of point $B$ are $(-1, -5)$.

Would you like more details or have any questions?

Here are five related questions:

1. How do you find the midpoint if the coordinates of $A$ and $B$ are both unknown?
2. What is the formula for the distance between two points in a coordinate plane?
3. How would you calculate the coordinates of $A$ if the coordinates of $B$ and $M$ were given?
4. Can the midpoint formula be used in three-dimensional space? How would that formula look?
5. How does the midpoint relate to the concept of the centroid in a triangle?

Tip: When dealing with midpoints, always double-check your arithmetic operations to ensure accuracy in finding the unknown coordinates.