The vertices of a parallelogram `A B C D` are `A(3,1),B(13 ,6),C(13 ,21),` and `D(3,16)dot` If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is (a) `(11)/(12)` (b) `(11)/8` (c) `(25)/8` (d) `(13)/8`

Options

A. `11//12`
B. `11//8`
C. `25//8`
D. `13//8`

Answer

B

Explanation

Slope of line thorugh origin is,
`m=(21-x)/(13)=(x+1)/(3)`
or ` 63-3x=13x+13`
or `16x=50`
or ` x=(25)/(8)`
Hence, `m=((25)/(8)+1)xx(1)/(3)`
`=(33)/(24)=(11)/(8)`