Question

If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______

Options

• `pi/3`

• `pi/2`

• `(3pi)/2`

• `pi/4`

Answer 1

If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is `underline(pi/4)`.

Explanation:

Here,

Slope of I^st diagonal = `m_1 = (4 - 2)/(4 - 2) = 1`

⇒ `theta_1 = 45^circ`

Slope of II^nd diagonal = `m_2 = (4 - 2)/(3 - 3) = ∞`

⇒ `theta_2 = 90^circ`

⇒ `theta_2 - theta_1 = 45^circ = pi/4`