if θ is the angle between the diagonals of a parallelogram ABCD whos

1.	if θ is the angle between the diagonals of a parallelogram ABCD whosevertices are A(0, 2), B(2,-1), C(40 and D( 2, 3). Show that tan θ=2
Answer» Point A lies in the y axis ( x = 0) Point C is int the x axis ( y = 0 ) Point B and D are in the line x = 2 . ( hence it is parallel to y axis . The diagonal AC intersects the parallel lines x = 0 and x = 2 Hence the angle it makes with the y axis is the angle θ ,(the angle between the diagonals ) AC cuts the y axis at y = 2 and x axis at x = 4 hence tan θ = 4/2 = 2

if θ is the angle between the diagonals of a parallelogram ABCD whosevertices are A(0, 2), B(2,-1), C(40 and D( 2, 3). Show that tan θ=2

Answer»

Point A lies in the y axis ( x = 0)

Point C is int the x axis ( y = 0 )

Point B and D are in the line x = 2 . ( hence it is parallel to y axis .

The diagonal AC intersects the parallel lines x = 0 and x = 2

Hence the angle it makes with the y axis is the angle θ ,(the angle between the diagonals )

AC cuts the y axis at y = 2 and x axis at x = 4

hence tan θ = 4/2 = 2