AP EAMCET · Maths · Straight Lines

When the coordinate axes are rotated through an angle $135 °$ , the coordinates of a point $P$ in the new system are known to be $(4, - 3)$ . Then find the coordinates of $P$ in the original system.

A $(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$
B $(\frac{- 1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$
C $(\frac{1}{\sqrt{2}}, \frac{- 7}{\sqrt{2}})$
D $(\frac{- 1}{\sqrt{2}}, \frac{- 7}{\sqrt{2}})$

Verified Solution

Answer & Solution

Correct Answer

(B) $(\frac{- 1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$

Step-by-step Solution

Detailed explanation

Let, we have a point Px, y, Now, the coordinate axes rotated through an angle 135°, and the coordinate of the point P in new system is 4, -3. Hence, applying the formula, the coordinates of the point P in the original system is…

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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When the coordinate axes are rotated through an angle 135°, the coordinates of a point P in the new system are known to be (4,-3). Then find the coordinates of P in the original system.

Step-by-step Solution

When the coordinate axes are rotated through an angle $135 °$ , the coordinates of a point $P$ in the new system are known to be $(4, - 3)$ . Then find the coordinates of $P$ in the original system.