A triangle has a vertex at (1, 2) and the mid-points of the two sides through it are and . Then, the centroid of this triangle is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: B
Solution
Let vertex A = (1,2). The midpoints of the two sides through A are M₁ = (-1,1) and M₂ = (2,3).
Since M₁ is the midpoint of AB: B = (2(-1)-1, 2(1)-2) = (-3, 0).
Since M₂ is the midpoint of AC: C = (2(2)-1, 2(3)-2) = (3, 4).
Centroid = ((1+(-3)+3)/3, (2+0+4)/3) = (1/3, 6/3) = (1/3, 2).
Since M₁ is the midpoint of AB: B = (2(-1)-1, 2(1)-2) = (-3, 0).
Since M₂ is the midpoint of AC: C = (2(2)-1, 2(3)-2) = (3, 4).
Centroid = ((1+(-3)+3)/3, (2+0+4)/3) = (1/3, 6/3) = (1/3, 2).
[JEE Main 2019 · 12 Apr · Shift II]