Question

he midpoint of start overline, AB, end overline
AB
is M, left parenthesis, minus, 4, comma, 2, right parenthesisM(−4,2). If the coordinates of AA are left parenthesis, minus, 7, comma, 3, right parenthesis(−7,3), what are the coordinates of BB?

Answer 1

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

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

We know:

- \( M(-4, 2) \)
- \( A(-7, 3) \)

Let the coordinates of \( B \) be \( (x, y) \). Plugging in the values we have:

1. For the x-coordinate of the midpoint:
\[
-4 = \frac{-7 + x}{2}
\]

Multiplying both sides by 2:
\[
-8 = -7 + x
\]

Solving for \( x \):
\[
x = -8 + 7 = -1
\]

2. For the y-coordinate of the midpoint:
\[
2 = \frac{3 + y}{2}
\]

Multiplying both sides by 2:
\[
4 = 3 + y
\]

Solving for \( y \):
\[
y = 4 - 3 = 1
\]

Thus, the coordinates of point \( B \) are \( (-1, 1) \).

Final answer: \( B(-1, 1) \)