Question

Use the midpoint formula to find B if A is (–4, 7) and the midpoint of the line segment AB is (0, 1).

Answer 1

To find point B using the midpoint formula, we start with the formula for the midpoint \( M \) of a segment connecting points \( A(x_1, y_1) \) and \( B(x_2, y_2) \):

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

In this case, we are given:
- Point \( A(-4, 7) \)
- Midpoint \( M(0, 1) \)

Let the coordinates of point B be \( (x_B, y_B) \). We know the following based on the midpoint formula:

\[
\left( \frac{-4 + x_B}{2}, \frac{7 + y_B}{2} \right) = (0, 1)
\]

This gives us two equations to solve:

1. From the x-coordinates:
\[
\frac{-4 + x_B}{2} = 0
\]
Multiplying both sides by 2:
\[
-4 + x_B = 0
\]
Adding 4 to both sides:
\[
x_B = 4
\]

2. From the y-coordinates:
\[
\frac{7 + y_B}{2} = 1
\]
Multiplying both sides by 2:
\[
7 + y_B = 2
\]
Subtracting 7 from both sides:
\[
y_B = 2 - 7 = -5
\]

So, the coordinates of point B are:
\[
B(4, -5)
\]

Thus, the final answer is:
\[
B = (4, -5)
\]