Question

In a triangle ABC, AB is parallel to y-axis, BC is parallel to x-axis, centroid is at (2, 1), If median through C is `x-y=1`, then the slope of median through A is
A. 2
B. 3
C. 4
D. 5

Answer 1

Correct Answer - C
Let `B(a,b), C(c,b), A (a,d)`.
Then D (mid point of BC) is `((a+c)/(2),b)`
E (mid point of AB) is `(a,(b+d)/(2))`
Given slope of `CE = 1 rArr (b-(b+d)/(2))/(c-a) =1rArr ((b-d))/(c-a) =2`
Slope of `AD = (b-d)/((a+c)/(2)-a) =2 ((b-d))/(c-a) =4`