Given:
Vertices of the triangle are (7, 2), (5, -2), and (-1, 0).

To prove:
The perpendicular bisectors of the sides of the triangle are concurrent.

Proof:

Step 1: Find the midpoints of all three sides of the triangle.
The midpoint of the side formed by (7, 2) and (5, -2) is:
((7 + 5)/2, (2 + (-2))/2) = (6, 0)

The midpoint of the side formed by (5, -2) and (-1, 0) is:
((5 + (-1))/2, (-2 + 0)/2) = (2, -1)

The midpoint of the side formed by (-1, 0) and (7, 2) is:
((-1 + 7)/2, (0 + 2)/2) = (3, 1)

Step 2: Find the slopes of the sides of the triangle.
The slope of the side formed by (7, 2) and (5, -2) is:
(2 - (-2))/(7 - 5) = 4/2 = 2

The slope of the side formed by (5, -2) and (-1, 0) is:
(-2 - 0)/(5 - (-1)) = -2/6 = -1/3

The slope of the side formed by (-1, 0) and (7, 2) is:
(0 - 2)/(-1 - 7) = -2/(-8) = 1/4

Step 3: Find the negative reciprocal of the slopes.
The negative reciprocal of 2 is -1/2.
The negative reciprocal of -1/3 is 3.
The negative reciprocal of 1/4 is -4.

Step 4: Find the equations of the perpendicular bisectors.
The equation of the perpendicular bisector of the side formed by (7, 2) and (5, -2) is:
y - 0 = (-1/2)(x - 6)
=> 2y = -x + 3
=> x + 2y - 3 = 0

The equation of the perpendicular bisector of the side formed by (5, -2) and (-1, 0) is:
y - (-1) = 3(x - 2)
=> y + 1 = 3x - 6
=> 3x - y - 7 = 0

The equation of the perpendicular bisector of the side formed by (-1, 0) and (7, 2) is:
y - 1 = (-4)(x - 3)
=> y - 1 = -4x + 12
=> 4x + y - 13 = 0

Step 5: Find the point of concurrence.
To find the point of concurrence, we need to solve the system of equations formed by the three perpendicular bisectors.

By solving the equations x + 2y - 3 = 0, 3x - y - 7 = 0, and 4x