Final answer:
The coordinates of the midpoint E are found by averaging the x-coordinates and y-coordinates of points A(-3a, b) and C(-a, -5b). After performing the calculations, the coordinates of midpoint E are (-2a, -2b). Therefore, the correct answer is C) (-2a, -2b).
Step-by-step explanation:
To find the coordinates of the midpoint E of the line segment with endpoints A(-3a, b) and C(-a, -5b), we use the midpoint formula, which is the average of the x-coordinates and the y-coordinates of the two points. The formula is:
Midpoint E = ((x1 + x2) / 2, (y1 + y2) / 2)
Substituting the given points A(-3a, b) and C(-a, -5b) into the formula gives us:
Midpoint E = (((-3a) + (-a)) / 2, (b + (-5b)) / 2)
This simplifies to:
Midpoint E = ((-3a - a) / 2, (b - 5b) / 2)
Therefore, the coordinates of midpoint E are:
Midpoint E = (-2a, -2b)
Looking at our answer choices, we see that the correct answer is C) (-2a, -2b).