TS EAMCET · Maths · Straight Lines

The centroid of the triangle formed by the lines $x - 3 y + 3 = 0, x + 3 y + 3 = 0, x + y - 1 = 0$ is

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

Verified Solution

Answer & Solution

Correct Answer

(A) $(0, \frac{- 1}{3})$

Step-by-step Solution

Detailed explanation

Asumming intersection of line x-3y+3=0 & x+3y+3=0 be A Now intersection of line x+3y+3=0 & x+y-1=0 be B And intersection of line x-3y+3=0 & x+y-1=0 be C, Now finding the point A, B & C by intersecting point we get,…

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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The centroid of the triangle formed by the lines x-3y+3=0,x+3y+3=0,x+y-1=0 is

Step-by-step Solution

The centroid of the triangle formed by the lines $x - 3 y + 3 = 0, x + 3 y + 3 = 0, x + y - 1 = 0$ is