TS EAMCET · Maths · Straight Lines

Let $L_{1}$ be a line passing through $(2, 1)$ and $(3, \frac{5}{2}) . L_{2}$ is a line perpendicular to $L_{1}$ and passing through $(4, - 1) .$ The area of the triangle formed by $L_{1}, L_{2}$ and $y$ -axis is

A $\frac{121}{39}$
B $\frac{121}{13}$
C $\frac{154}{169}$
D $\frac{22}{13}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{121}{39}$

Step-by-step Solution

Detailed explanation

Line L1 is passing through 2,1 and 3,52 Line L2 is passing through 4,-1 and perpendicular to L1 Two point form of the straight line is y-y1=y2-y1x2-x1x-x1 L1: y-1=52-13-2x-2 L1:3x-2y=4 Since the lines L1 and L2 are perpendicular and we know that if two lines…

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.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

Let L1 be a line passing through 2,1 and 3, 52.L2 is a line perpendicular to L1 and passing through 4,-1. The area of the triangle formed by L1, L2 and y-axis is

Step-by-step Solution

Let $L_{1}$ be a line passing through $(2, 1)$ and $(3, \frac{5}{2}) . L_{2}$ is a line perpendicular to $L_{1}$ and passing through $(4, - 1) .$ The area of the triangle formed by $L_{1}, L_{2}$ and $y$ -axis is