If a line segment has endpoints A(3x+5,3y) and B(x-1,-y), what are the coordinates of the midpoint of line segment AB?

The midpoint of a line segment is just halfway from A to B. So, the coordinates are just the average of the endpoints.

If C = midpoint of AB then

C = ((3x+5 + x-1)/2,(3y + -y)/2)
= ((4x+4)/2,2y/2) = (2x+2,y)

To find the coordinates of the midpoint of line segment AB, we need to find the average of the x-coordinates and the average of the y-coordinates of the endpoints. The midpoint (M) is given by:

M((x1+x2)/2, (y1+y2)/2)

In our case, the coordinates of endpoint A are (3x+5, 3y), and the coordinates of endpoint B are (x-1, -y). Using the formula above, we can find the midpoint as follows:

Midpoint (M): ((3x+5 + x-1)/2, (3y+(-y))/2)

Simplifying further:

Midpoint (M): ((4x+4)/2, (2y)/2)

Midpoint (M): (2x+2, y)

Therefore, the coordinates of the midpoint of line segment AB are (2x+2, y).

To find the midpoint of a line segment, you need to average the coordinates of its endpoints.

Given that the endpoints of line segment AB are A(3x+5,3y) and B(x-1,-y), we can find the midpoint by averaging their coordinates.

The x-coordinate of the midpoint is the average of the x-coordinates of A and B:
x-coordinate of the midpoint = (3x+5 + x-1) / 2

Simplifying this expression, we get:
x-coordinate of the midpoint = (4x + 4) / 2
x-coordinate of the midpoint = 2x + 2

Similarly, the y-coordinate of the midpoint is the average of the y-coordinates of A and B:
y-coordinate of the midpoint = (3y + (-y)) / 2
y-coordinate of the midpoint = (2y) / 2
y-coordinate of the midpoint = y

Therefore, the coordinates of the midpoint of line segment AB are:
(x, y) = (2x + 2, y)