(i) Find the gradient of a straight line which is passes through the point (-3. 6) and the mid point of (4,-5) and (-2, 9)

Options

A. `(pi)/(4)`
B. `(pi)/(6)`
C. `(pi)/(3)`
D. `(3pi)/(4)`

Answer

D

Explanation

The coordinates of the mid-point D of the segment BC are (1,2).
`therefore ` Slope of AD`=(6-2)/(-3-1)=-1`
`implies theta =-1` , where `theta` is the angle made by AD with x-axis
`implies theta=(3pi)/(4)`
So, AD makes angles `(3pi)/(4)` with x -axis