23B. If θ is the angle between the diagonals of a parallelogram ABCD

1.	23B. If θ is the angle between the diagonals of a parallelogram ABCD whosevertices are A(0, 2), B(2,-1), C(4, 0) and D(2, 3). Show that tan 0 2
Answer» In the parallelogram ABCD, Slope of the diagonalAC (m1) = (0-2)/ (4-0) = -1/2 Slope of the diagonal BD (m2) = (3 - (-1))/ (2 - 2 ) = ∞ That means diagonal BD is parallel to the y axis. Now, m1x m2= -1 (-1/2) x tanθ = -1 So, tan θ = 2

23B. If θ is the angle between the diagonals of a parallelogram ABCD whosevertices are A(0, 2), B(2,-1), C(4, 0) and D(2, 3). Show that tan 0 2

Answer»

In the parallelogram ABCD,

Slope of the diagonalAC (m1) = (0-2)/ (4-0) = -1/2

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

That means diagonal BD is parallel to the y axis.

Now, m1x m2= -1

(-1/2) x tanθ = -1

So, tan θ = 2