Question

The vertices A and C of rhombus ABCD are A = (3, −1) and C = (−4, –8). The slope of the diagonal BD is ______.

Options

• 7

• −7

• 1

• −1

Answer 1

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

Explanation:

By formula,

Slope = `(y_2 − y_1)/(x_2 − x_1)`

Slope of AC = `(−8−(−1))/(−4−3) = (−8+1)/(−7) = (−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