TS EAMCET · Maths · Three Dimensional Geometry

If the mid points of the sides $A B, B C$ and $C A$ of a triangle are respectively $D (1, 2, - 3),$ $E (3, 0, 1)$ and $F (- 1, 1, - 4),$ then the centroid of the triangle $A D F$ is

A $(- 1, 2, - 5)$
B $(3, \frac{5}{3}, \frac{- 2}{3})$
C $(1, 0, - 3)$
D $(- 1, \frac{5}{3}, - 3)$

Verified Solution

Answer & Solution

Correct Answer

(A) $(- 1, 2, - 5)$

Step-by-step Solution

Detailed explanation

Given: Mid-point of the sides of a triangle AB, BC, CA are D1,2,-3, E3,0,1, F-1,1,-4 Let the vertices of ∆ABC Ax1,y2,z1, Bx2,y2,z2, Cx3,y3,z3 and D is the mid-point of AB then Co-ordinate of point D is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the mid points of the sides AB, BC and CA of a triangle are respectively D1, 2, -3, E3, 0, 1 and F-1, 1, -4, then the centroid of the triangle ADF is

Step-by-step Solution

If the mid points of the sides $A B, B C$ and $C A$ of a triangle are respectively $D (1, 2, - 3),$ $E (3, 0, 1)$ and $F (- 1, 1, - 4),$ then the centroid of the triangle $A D F$ is