Question

In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of ΔABC (in sq. units) is 

(A) 12 

(B) 4 

(C) 5 

(D) 9

Answer 1

Answer is (D) 9

We draw the triangle ABC as shown in the following figure:

The centroid G is (4, 1). 

Let coordinate of B C (α, 5 - α)  and (4, β).

The midpoint of AB is the median of ∠C and it has value

M((α + 1)/2, (1 - α)/2).

So, (α + 1)/2 = 4 ⇒ α = 7

Similarly, midpoint of AC is the median of ∠B and it has the value N(5/2, (β + 2)/2).