In ABC , if A =(1,2) and the equations of the medians through B and C are x+y=5 and x=4 respectively, then the area of ABC is

Step-by-step solution

OC & OB the equations of medians respectively and point O is the centroid. Intersection OC & OB is centroid. Solving x+y=5 & x=4 , we get the centroid as (4,1) . Let the coordinate of point C=(4, a) and coordinate of point B=(b, 5-b) So, 1+4+b 3 =4 b=7 2+a+5-b 3 =1 a=3 A=(1,2) ; B=(7,-2) ; C=(4,3) = 1 2 | array ccc 1 & 1 & 2 1 & 7 & -2 1 & 4 & 3 array | = 1 2 18=9