Question

The midpoint of start overline, AB, end overline AB is M, left parenthesis, minus, 3, comma, 0, right parenthesisM(−3,0). If the coordinates of AA are left parenthesis, minus, 5, comma, 3, right parenthesis(−5,3), what are the coordinates of BB?

Answer 1

To find the coordinates of point \( B \), we can use the formula for the midpoint of a line segment. The coordinates of the midpoint \( M(x_m, y_m) \) between two points \( A(x_a, y_a) \) and \( B(x_b, y_b) \) are given by:

\[
x_m = \frac{x_a + x_b}{2}
\]
\[
y_m = \frac{y_a + y_b}{2}
\]

We are given:
- The midpoint \( M(-3, 0) \)
- The coordinates of point \( A(-5, 3) \)

Let the coordinates of point \( B \) be \( (x_b, y_b) \). From the midpoint coordinates, we can set up the following equations:

1. For the \( x \)-coordinate:
\[
-3 = \frac{-5 + x_b}{2}
\]

2. For the \( y \)-coordinate:
\[
0 = \frac{3 + y_b}{2}
\]

Now, we will solve these equations.

**Solving for \( x_b \):**
From the first equation:
\[
-3 = \frac{-5 + x_b}{2}
\]
Multiplying both sides by 2:
\[
-6 = -5 + x_b
\]
Adding 5 to both sides:
\[
x_b = -6 + 5 = -1
\]

**Solving for \( y_b \):**
From the second equation:
\[
0 = \frac{3 + y_b}{2}
\]
Multiplying both sides by 2:
\[
0 = 3 + y_b
\]
Subtracting 3 from both sides:
\[
y_b = -3
\]

Thus, the coordinates of point \( B \) are:
\[
B(-1, -3)
\]

**Final Answer:**
The coordinates of point \( B \) are \( (-1, -3) \).