Final answer:
To find the coordinates of point B, we used the midpoint formula, given the midpoint M(-4, 0) and point A(-6, 6). After solving two equations, we determined that the coordinates of B are (-2, -6).
Step-by-step explanation:
To determine the coordinates of point B given that M is the midpoint of segment AB with the coordinates of A provided, we use the midpoint formula. The midpoint M is calculated using the formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Since we are given M(-4, 0) and A(-6, 6), we can set up the equations:
-4 = (-6 + x2)/2
0 = (6 + y2)/2
By solving these two equations, we can find x2 and y2, the coordinates of point B. Multiplying both sides by 2 to clear the fractions, we get:
-8 = -6 + x2 and 0 = 6 + y2
Isolating x2 and y2 gives us the coordinates for B:
x2 = -8 + 6 = -2
y2 = 0 - 6 = -6
So the coordinates of point B are (-2, -6).