To find the coordinates of point $B$, we can use the midpoint formula. The midpoint $M$ 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:

• Midpoint $M(-4, 4)$
• Coordinates of $A(-3, 1)$

Let the coordinates of point $B$ be $(x, y)$. Plugging in the known values into the midpoint formula:

$(-4, 4) = \left(\frac{-3 + x}{2}, \frac{1 + y}{2}\right)$

We can separate these into two equations:

1. $\frac{-3 + x}{2} = -4$
2. $\frac{1 + y}{2} = 4$

Solving for $x$:

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

Multiply both sides by 2:

$-3 + x = -8$

Add 3 to both sides:

$x = -5$

Solving for $y$:

$\frac{1 + y}{2} = 4$

Multiply both sides by 2:

$1 + y = 8$

Subtract 1 from both sides:

$y = 7$

Coordinates of $B$:

$B(-5, 7)$

Would you like any further details or have any questions? Here are some related questions you might explore:

1. How do you find the midpoint if given coordinates of both endpoints?
2. What is the distance formula between two points?
3. How would the midpoint change if the coordinates of $A$ or $B$ were altered?
4. Can the midpoint formula be applied in three-dimensional space?
5. What are some real-world applications of finding midpoints?

Tip: Always verify your calculations by substituting the coordinates back into the original formula to ensure consistency.