**Solution:**

To find the equation of the other diagonal of the square, we need to determine the coordinates of the other two vertices. Let's call the given vertex (-4,5) as A.

**Step 1: Finding the coordinates of the other two vertices**

Since a square has four equal sides, we can determine the coordinates of the other two vertices by applying a series of geometric transformations.

**Translation:**
We can translate vertex A by the length of one side to find vertex B. Since the square has four equal sides, the length of one side can be found using the distance formula.

The distance between A (-4,5) and B (x,y) is given by the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

Using the coordinates (-4,5) for A and (x,y) for B, we have:

d = √[(x - (-4))^2 + (y - 5)^2]

Since it is a square, the length of one side will be equal to the diagonal divided by √2. So we have:

d = diagonal/√2

Substituting the given diagonal equation 7x - y + 8 = 0, we can solve for d:

7x - y + 8 = 0
y = 7x + 8

Substituting y = 7x + 8 into the distance formula, we have:

d = √[(x - (-4))^2 + ((7x + 8) - 5)^2]

Simplifying the equation inside the square root:

d = √[(x + 4)^2 + (7x + 3)^2]

Since d = diagonal/√2, we can write the equation as:

diagonal/√2 = √[(x + 4)^2 + (7x + 3)^2]

Squaring both sides to eliminate the square root:

diagonal^2/2 = (x + 4)^2 + (7x + 3)^2

Expanding and simplifying:

diagonal^2/2 = x^2 + 8x + 16 + 49x^2 + 42x + 9

diagonal^2/2 = 50x^2 + 50x + 25

Multiplying both sides by 2 to eliminate the fraction:

diagonal^2 = 100x^2 + 100x + 50

**Step 2: Finding the coordinates of the other two vertices (cont.)**

Now that we have an equation for the diagonal, we can solve it to find the coordinates of the other two vertices.

Let's assume the coordinates of vertex B are (p,q).

Using the equation of the diagonal:

diagonal^2 = 100p^2 + 100p + 50

Substituting the values of the given diagonal (-4,5) and simplifying:

(7(-4) - 5 + 8)^2 = 100p^2 + 100p + 50

(-28 - 5 + 8)^2 = 100p^2 + 100p + 50

(-25)^2 = 100p^2 + 100p + 50

625 = 100p^

first find slope by eq. and then find slope of normal and by slope point form find eq.