The midpoint of start overline, AB, end overline 
AB
  is M, left parenthesis, 0, comma, 2, right parenthesisM(0,2). If the coordinates of AA are left parenthesis, 5, comma, minus, 1, right parenthesis(5,−1), what are the coordinates of BB?

To find the coordinates of point \( B \), given that \( M(0, 2) \) is the midpoint of \( \overline{AB} \) and \( A(5, -1) \) is one of the endpoints, we use the midpoint formula.

The midpoint formula states that for two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), the midpoint \( M(x_m, y_m) \) is given by:

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

Given:
- Midpoint \( M(0, 2) \)
- Point \( A(5, -1) \)

Let's denote the coordinates of point \( B \) as \( (x_2, y_2) \).

### Step 1: Set up the equations
Using the midpoint formula, we have:
\[
0 = \frac{5 + x_2}{2} \quad \text{(for the x-coordinate)}
\]
\[
2 = \frac{-1 + y_2}{2} \quad \text{(for the y-coordinate)}
\]

### Step 2: Solve for \( x_2 \) and \( y_2 \)
1. Solving for \( x_2 \):
\[
0 = \frac{5 + x_2}{2}
\]
Multiply both sides by 2:
\[
0 = 5 + x_2
\]
Subtract 5 from both sides:
\[
x_2 = -5
\]

2. Solving for \( y_2 \):
\[
2 = \frac{-1 + y_2}{2}
\]
Multiply both sides by 2:
\[
4 = -1 + y_2
\]
Add 1 to both sides:
\[
y_2 = 5
\]

### Final Answer
The coordinates of point \( B \) are \( (-5, 5) \).

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:
1. How would you find the distance between points \( A \) and \( B \)?
2. What is the slope of the line segment \( \overline{AB} \)?
3. How would you find the equation of the line that passes through points \( A \) and \( B \)?
4. If \( B \) was at \( (-5, 5) \), what would be the length of the line segment \( \overline{AB} \)?
5. How would the midpoint formula change in three dimensions?

**Tip:** The midpoint formula can also be extended to higher dimensions, such as 3D, where you average the coordinates of all dimensions.

The midpoint of line segment AB is M(0, 2). If the coordinates of A are (5, -1), what are the coordinates of B?

Learn how to find the coordinates of a point using the midpoint formula. This problem involves coordinate geometry concepts and step-by-step calculations to determine point B's coordinates given the midpoint and one endpoint. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation