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:
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From the x-coordinates: \[ \frac{-4 + x_B}{2} = 0 \] Multiplying both sides by 2: \[ -4 + x_B = 0 \] Adding 4 to both sides: \[ x_B = 4 \]
-
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: \[ B = (4, -5) \]