To find the midpoint of a line segment defined by two endpoints, we can use the midpoint formula. The formula is as follows:
Midpoint (M) = ( (x1 + x2) / 2, (y1 + y2) / 2 )
In this formula, (x1, y1) are the coordinates of the first endpoint (A), and (x2, y2) are the coordinates of the second endpoint (B).
For our given endpoints:
- A(4, 13): x1 = 4, y1 = 13
- B(6, 5): x2 = 6, y2 = 5
Now we can substitute these values into the midpoint formula:
1. For the x-coordinate of the midpoint:
xM = (x1 + x2) / 2 = (4 + 6) / 2 = 10 / 2 = 5
2. For the y-coordinate of the midpoint:
yM = (y1 + y2) / 2 = (13 + 5) / 2 = 18 / 2 = 9
Combining these results, the midpoint M of the line segment AB is:
M(5, 9)
So, the midpoint of the line segment with endpoints A(4, 13) and B(6, 5) is M(5, 9).