To find the coordinates of point $B$ given the midpoint $M$ and the coordinates of point $A$, we can use the midpoint formula.

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 calculated as: $x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$

Given:

• Midpoint $M = (-3, 4)$
• Coordinates of $A = (-5, 1)$

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

Finding Coordinates of $B$

1. Find $x_2$:

$-3 = \frac{-5 + x_2}{2}$

Multiply both sides by 2:

$-6 = -5 + x_2$

Solve for $x_2$:

$x_2 = -6 + 5 = -1$

2. Find $y_2$:

$4 = \frac{1 + y_2}{2}$

Multiply both sides by 2:

$8 = 1 + y_2$

Solve for $y_2$:

$y_2 = 8 - 1 = 7$

Coordinates of $B$

The coordinates of point $B$ are:

$B(-1, 7)$

Would you like more details on how to solve this or have any other questions?

Here are 5 related questions you might find interesting:

1. How do you find the distance between two points in a coordinate plane?
2. What is the formula for the slope of a line segment between two points?
3. How do you find the equation of a line given two points?
4. What is the reflection of a point across the origin?
5. How do you determine if three points are collinear?

Tip: Always double-check your calculations when solving for coordinates to avoid simple mistakes.