Question

if x-2y+k=0 is a median of the triangle whose vertices are at points A(-1,3),B(0,4),C(-5,2),FIND THE VALUE OF K

Answer 1

Median is  a line which passes through the vertex of a triangle  divides the opposite side in the ratio 1:1 .
If we take the following cases 
CASE1:
If AD is the median then it must pass through the midpoint of B and C 
so applying midpoint formula
($x_{1}$+$x_{2}$/2,$y_{1}$+$y_{2}$/2)
∴ D≡(-5/2,3) So it satisfies the median AD 
∴ -5/2-2*3+K=0 ⇒k=17/2
CASE 2:
If BE is the median then it must pass  through the midpoint of A and C 
∴E≡(-3,5/2) So it satisfies the equation of median 
-3-2*5/2+k=0  ⇒k=8
CASE 3 
If CF is the median where F is the midpoint of A and B 
∴It satisfies the equation median 
-1/2-2*7/2+k=0
∴ k=15/2

Answer 2

plz refer to this attachment