The line through the points `(-2, a) and (9, 3)`has slope `(-1)/(2)`. Find the value of a.

Options

A. `(-(9)/(2),9,9)`
B. `((9)/(2),9,9)`
C. `(9,-(9)/(2),9)`
D. `(9,(9)/(2),9)`

Answer

a

Explanation

Direction ratios of the joining points `P(1, 2, 3) and Q(-3, 4, 5)` are -4, 2, 2 which are the direction ratio of the normal to the plane.
Then, equation of plane is `-4x+2y+2z=k`.
Also this plane passes through the midpoint of `PQ(-1, 3, 4)`. Thus,
`" "-4(-1)+ 2(3)+ 2(4)=k`
or `" "k=18`
Hence, equation of plane is `2x-y-z=-9`
Then, intercepts are `(-9//2), 9 and 9`