TS EAMCET · Maths · Straight Lines

If the line $x - y + 1 = 0$ cuts the lines $2 x + 2 y + 3 = 0$ and $3 x + 3 y + 2 = 0$ at the points $A$ and $B$ respectively, then $A B =$

A $\frac{5}{6 \sqrt{2}}$
B $\frac{1}{6 \sqrt{2}}$
C $\frac{5}{\sqrt{3}}$
D $\frac{5}{6 \sqrt{3}}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{5}{6 \sqrt{2}}$

Step-by-step Solution

Detailed explanation

Given, The line x-y+1=0 cuts the lines 2x+2y+3=0 and 3x+3y+2=0 at the points A and B respectively, Now we can see that 2x+2y+3=0 slope =1 and 3x+3y+2=0 slope =1 are parallel lines as their slopes are equal, Now line x-y+1=0 has slope =-1, So x-y+1=0 is perpendicular to both…

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 line x-y+1=0 cuts the lines 2x+2y+3=0 and 3x+3y+2=0 at the points A and B respectively, then AB=

Step-by-step Solution

If the line $x - y + 1 = 0$ cuts the lines $2 x + 2 y + 3 = 0$ and $3 x + 3 y + 2 = 0$ at the points $A$ and $B$ respectively, then $A B =$