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

The midpoint $M(x_m, y_m)$ of a line segment connecting two points $A(x_a, y_a)$ and $B(x_b, y_b)$ is given by the formula:

$M = \left( \frac{x_a + x_b}{2}, \frac{y_a + y_b}{2} \right)$

We know:

• The midpoint $M = (-2, 4)$,
• The coordinates of point $A = (-1, 5)$.

Let the coordinates of point $B$ be $(x_b, y_b)$.

Using the midpoint formula, we can set up two equations:

1. For the $x$-coordinates: $\frac{-1 + x_b}{2} = -2$ Multiplying both sides by 2: $-1 + x_b = -4$ Solving for $x_b$: $x_b = -4 + 1 = -3$

2. For the $y$-coordinates: $\frac{5 + y_b}{2} = 4$ Multiplying both sides by 2: $5 + y_b = 8$ Solving for $y_b$: $y_b = 8 - 5 = 3$

Thus, the coordinates of point $B$ are $(-3, 3)$.

Would you like a detailed explanation of the midpoint formula or have any other questions?

Here are 5 related questions:

1. What is the distance between points $A$ and $B$?
2. How can you find the slope of line segment $AB$?
3. If the line segment $AB$ is extended beyond point $B$, what would the coordinates of a point $C$ be, such that $B$ is the midpoint of $AC$?
4. How do you find the equation of the line passing through points $A$ and $B$?
5. What is the general formula for finding the center of mass of two points in a plane?

Tip: The midpoint formula is very useful in geometry, especially when dividing line segments in half or finding the center between two points.