A(7, -8) and C(1, 4) are vertices of a square ABCD. Find equation of diagonal BD?

Answer: Option B

By the midpoint formula, $$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$
Midpoint of line AC $$=\left(\frac{7+1}{2},\frac{-8+4}{2}\right)=\left(4,-2\right)$$
O(x₃, y₃) = (4, -2)
(M₁) Slope of line AC,
$$M_1=\frac{y_2-y_1}{x_2-x_1}=\frac{4-\left(-8\right)}{1-7}=-2$$
If the lines are ⊥, then M₁ × M₂ = -1
- 2 × M₂ = -1
M₂ = $$\frac{1}{2}$$
∴ Equation of line BD
y - y₃ = M₂(x - x₃)
y - (-2) = $$\frac{1}{2}$$(x - 4)
y + 2 = $$\frac{1}{2}$$(x - 4)
x - 2y = 8