To find the coordinates of $B(x_B, y_B)$, we will use the midpoint formula.

The midpoint formula states: $M = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)$ Where:

• $M$ is the midpoint,
• $A(x_A, y_A)$ and $B(x_B, y_B)$ are the coordinates of points $A$ and $B$, respectively.

In this problem:

• The midpoint $M$ is given as $(-7, 4)$,
• The coordinates of point $A$ are $(-6, 7)$.

Now, we will plug these values into the midpoint formula:

1. For the $x$-coordinates: $-7 = \frac{-6 + x_B}{2}$ Multiply both sides by 2: $-14 = -6 + x_B$ Add 6 to both sides: $x_B = -14 + 6 = -8$

2. For the $y$-coordinates: $4 = \frac{7 + y_B}{2}$ Multiply both sides by 2: $8 = 7 + y_B$ Subtract 7 from both sides: $y_B = 8 - 7 = 1$

Thus, the coordinates of point $B$ are $(-8, 1)$.

Would you like further details or clarifications?

Here are 5 related questions:

1. How do you find the distance between two points?
2. How would the midpoint formula change in 3D space?
3. Can you verify the result by using the distance formula between $A$ and $B$?
4. How can you calculate the slope of line $AB$?
5. How does the midpoint relate to the equation of a line?

Tip: The midpoint formula can be applied in any dimension, just adapt it to the number of coordinates.