The midpoint of start overline, AB, end overline
AB
is M, left parenthesis, minus, 6, comma, 3, right parenthesisM(−6,3). If the coordinates of AA are left parenthesis, minus, 5, comma, 5, right parenthesis(−5,5), what are the coordinates of BB?

To find the coordinates of point \( B(x_2, y_2) \), we can use the midpoint formula. The midpoint \( M(x_m, y_m) \) of a line segment between points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

We know:
- \( M = (-6, 3) \)
- \( A = (-5, 5) \)

Using the midpoint formula for each coordinate:

### For the x-coordinate:
\[
-6 = \frac{-5 + x_2}{2}
\]

Multiply both sides by 2:
\[
-12 = -5 + x_2
\]

Solve for \( x_2 \):
\[
x_2 = -12 + 5 = -7
\]

### For the y-coordinate:
\[
3 = \frac{5 + y_2}{2}
\]

Multiply both sides by 2:
\[
6 = 5 + y_2
\]

Solve for \( y_2 \):
\[
y_2 = 6 - 5 = 1
\]

### Final Answer:
The coordinates of \( B \) are \( (-7, 1) \).

Would you like more details on this process?

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Here are 5 related questions to explore:
1. How do you find the midpoint of a line segment when both endpoints are given?
2. What is the geometric significance of the midpoint in a coordinate plane?
3. How can the midpoint formula be used to check if a line segment is bisected?
4. If you change the coordinates of point \( A \), how does it affect the midpoint?
5. How would you find the midpoint if one of the points is a variable, like \( A(x_1, y_1) \)?

**Tip:** Always double-check your work by plugging your calculated point back into the midpoint formula to verify accuracy.

The midpoint of AB is M(−6,3). If the coordinates of A are (−5,5), what are the coordinates of B?

Learn how to find the coordinates of point B given the midpoint M(-6,3) and point A(-5,5) using the midpoint formula. This problem covers key concepts in coordinate geometry, suitable for students in Grades 6-8.

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