TS EAMCET · Maths · Straight Lines

If $P^{'} (a, b)$ is the image of the point $P (- 1, 2)$ with respect to the line $x - 2 y + 3 = 0,$ then the length of the perpendicular from $P^{'}$ on to the line $2 x + y - 7 = 0$ is

A $\frac{3}{\sqrt{5}}$
B $5$
C $\frac{7}{\sqrt{5}}$
D $7$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{7}{\sqrt{5}}$

Step-by-step Solution

Detailed explanation

The image h,k of a point Px1,y1 about the line ax+by+c=0 is given by h-x1a=k-y1b=-2ax1+by1+ca2+b2 Now putting all values from the given data in this formula, we get a+11=b-2-2=-2-1-4+31+4 a=-15,b=25 Length of perpendicular from -15,25 on the line 2x+y-7=0 is given by…

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 P'(a, b) is the image of the point P(-1, 2) with respect to the line x-2y+3=0, then the length of the perpendicular from P' on to the line 2x+y-7=0 is

Step-by-step Solution

If $P^{'} (a, b)$ is the image of the point $P (- 1, 2)$ with respect to the line $x - 2 y + 3 = 0,$ then the length of the perpendicular from $P^{'}$ on to the line $2 x + y - 7 = 0$ is