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)