To prove that the point (2, -1) is the midpoint of the line joining the points (1, 5) and (3, -7), we need to show that the coordinates of the midpoint are indeed (2, -1).
The midpoint formula for two points (x₁, y₁) and (x₂, y₂) is given by:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Let's calculate the midpoint using the given points (1, 5) and (3, -7):
Midpoint = ((1 + 3)/2, (5 + (-7))/2)
Midpoint = (4/2, -2/2)
Midpoint = (2, -1)
As you can see, the coordinates of the midpoint (2, -1) match the given point (2, -1). Therefore, we have proved that the point (2, -1) is the midpoint of the line joining the points (1, 5) and (3, -7).