Question

Find the coordinates of midpoint E.

Given points A(-3a, b) and C(-a, -5b), what are the coordinates of the midpoint E?

A) (-3a - a, b - 5b)
B) (3a - a, b - 5b)
C) (-2a, -2b)
D) (a, -2b

Answer 1

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).