Point C is the midpoint of line AB. Point A has coordinates (2.4) and point C has coordinates (5,0). What are the coordinates of point B?

To find the coordinates of point \( B \), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint \( C(x_m, y_m) \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) are given by:

\[
x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}
\]

In this case:
- Point \( A \) has coordinates \( (2, 4) \)
- Point \( C \), the midpoint, has coordinates \( (5, 0) \)
  
Substituting into the midpoint formula:

\[
5 = \frac{2 + x_2}{2} \quad \text{and} \quad 0 = \frac{4 + y_2}{2}
\]

### Solving for \( x_2 \) and \( y_2 \):

1. For \( x_2 \):
\[
5 = \frac{2 + x_2}{2} \quad \Rightarrow \quad 10 = 2 + x_2 \quad \Rightarrow \quad x_2 = 8
\]

2. For \( y_2 \):
\[
0 = \frac{4 + y_2}{2} \quad \Rightarrow \quad 0 = 4 + y_2 \quad \Rightarrow \quad y_2 = -4
\]

Thus, the coordinates of point \( B \) are \( (8, -4) \).

Would you like any further clarification or details?

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Here are 5 related questions to deepen understanding:
1. How do you find the distance between points A and B?
2. What is the slope of line AB?
3. How would the problem change if point C wasn't the midpoint?
4. Can the midpoint formula be used in three dimensions? How?
5. What happens to the coordinates of point B if point A changes?

**Tip:** Always double-check your arithmetic when working with coordinates to avoid small errors in calculation!

Point C is the midpoint of line AB. Point A has coordinates (2,4) and point C has coordinates (5,0). What are the coordinates of point B?

Discover how to use the midpoint formula to find the coordinates of point B when given points A (2, 4) and C (5, 0) as the midpoint. This detailed solution breaks down the process step by step for students in Grades 6-8, helping them understand coordinate geometry concepts.

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