AP EAMCET · Maths · Straight Lines

Let $C$ be the centroid of the triangle with vertices $(3, - 1), (1, 3)$ and $(2, 4) .$ Let $P$ be the point of intersection of the lines $x + 3 y - 1 = 0$ and $3 x - y + 1 = 0 .$ Then the line passing through the points $C$ and $P$ also passes through the point

A $(- 9, - 7)$
B $(- 9, - 6)$
C $(7, 6)$
D $(9, 7)$

Verified Solution

Answer & Solution

Correct Answer

(B) $(- 9, - 6)$

Step-by-step Solution

Detailed explanation

The centroid of a triangle having vertices x1,y1, x2,y2 and x3,y3 is x1+x2+x33,y1+y2+y33. The centroid of the triangle having vertices (3,-1), (1,3) and (2,4) is C3+1+23,-1+3+43=(2,2). The equation of a line passing through the point on intersection of lines L1=0 and…

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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Let C be the centroid of the triangle with vertices (3,-1),(1,3) and (2,4). Let P be the point of intersection of the lines x+3 y-1=0 and 3 x-y+1=0. Then the line passing through the points C and P also passes through the point

Step-by-step Solution

Let $C$ be the centroid of the triangle with vertices $(3, - 1), (1, 3)$ and $(2, 4) .$ Let $P$ be the point of intersection of the lines $x + 3 y - 1 = 0$ and $3 x - y + 1 = 0 .$ Then the line passing through the points $C$ and $P$ also passes through the point