Question

If theta is the angle between the diagonals of a parallelogram ABCD whose vertices are A(0,2) B(2,-1) C(4,0) and D(2,3). Show that tan theta = 2.

Answer 1

the answer is either 2/√5 or √5/2 ....however it is not coming 2.....

Answer 2

Thank you for asking this question. Here is your answer:

In parallelogram ABCD

The slope of the diagonal AC (m₁) = (0-2) / (4-0)

= - 1/2

Slope of the diagonal BD (m₂) = (3-(-1) )/(2-2) = ∞

Diagonal BD is parallel to the y axis.

m₁ x m₂ = -1

(-1/2) x tanθ = 2

This is proved.

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