**Given Information:**
We are given three points which are the midpoints of the sides of triangle ABC: (3,-1) is the midpoint of side BC, (2,4) is the midpoint of side CA, and (-5,7) is the midpoint of side AB.

**Approach:**
To find the equation of side CA, we need two points on that side. We already have one point, which is the midpoint (2,4). Now, we need to find the other point.

**Step 1: Finding the coordinates of point A:**
Since (3,-1) is the midpoint of side BC, we can use the midpoint formula to find the coordinates of point A. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).

Let's use this formula to find the coordinates of point A:
(3,-1) = ((x₂ + x₃)/2, (y₂ + y₃)/2)

We are given that (3,-1) is the midpoint of side BC, so the coordinates of point C are (x₂, y₂) and the coordinates of point B are (x₃, y₃). Therefore:
(3,-1) = ((x₂ + x₃)/2, (y₂ + y₃)/2)

Simplifying the equation, we get:
6 = x₂ + x₃
-2 = y₂ + y₃

**Step 2: Finding the coordinates of point B:**
Since (-5,7) is the midpoint of side AB, we can use the midpoint formula again to find the coordinates of point B:
(-5,7) = ((x₁ + x₃)/2, (y₁ + y₃)/2)

We are given that (-5,7) is the midpoint of side AB, so the coordinates of point A are (x₁, y₁) and the coordinates of point C are (x₃, y₃). Therefore:
(-5,7) = ((x₁ + x₃)/2, (y₁ + y₃)/2)

Simplifying the equation, we get:
-10 = x₁ + x₃
14 = y₁ + y₃

**Step 3: Finding the equation of side CA:**
Now we have the coordinates of points A and B, which are (-10,14) and (6,-2) respectively. We can use these two points to find the equation of side CA using the slope-intercept form of a linear equation, y = mx + b.

Let's find the slope (m) first:
m = (y₂ - y₁)/(x₂ - x₁)
= (-2 - 14)/(6 - (-10))
= (-16)/(6 + 10)
= -16/16
= -1

Now, we can substitute the slope (m) and one of the points (x, y) into the slope-intercept form to find the y-intercept (b):
-2 = -1(6) + b
-2 = -6 + b
b = -2 + 6
b = 4

Therefore,