The vertices A and C of rhombus ABCD are A = (3, -1) and C = (-4, -8). The slope of diagonal BD is :

1. 7

2. -7

3. 1

4. -1

By formula,

Slope = $\dfrac{y$2 - y1}{x2 - x1}

Slope of AC = $\dfrac{-8 - (-1)}{-4 - 3} = \dfrac{-8 + 1}{-7} = \dfrac{-7}{-7}$ = 1.

We know that,

Diagonals of rhombus are perpendicular to each other.

Let slope of diagonal of BD be x.

We know that,

Product of slope of two perpendicular lines = -1.

∴ Slope of AC × Slope of BD = -1

⇒ 1 × Slope of BD = -1

⇒ Slope of BD = -1.

Hence, Option 4 is the correct option.