If the two sides of rhombus are `x+2y+2=0` and `2x+y-3=0,` then find the slope of the longer diagonal.

Answer

-1

Explanation

The diagonals of rhombus are along the angle bisectors of sides.
The bisector of the longer diagonal is that of acute angle bisector.
The given sides of rhombus are
`x+2y+2=0 " "(1)`
` "and " -2x-y+3 =0 " "(2)`
`"Now, a_(1)a_(2)+b_(1)b_(2) = -2-2 = -4 lt 0`
The acute angle bisector is
`(x+2y+2)/(5) = (-2x-y+3)/(5)`
or 3x+3y-1 = 0
Therefore, the slope of the longer diagonal is -1.