AP EAMCET · Maths · Straight Lines

When the axes are rotated through an angle $45 °$ , the new coordinates of a point $P$ are $(1, - 1)$ . The coordinates of $P$ in the original system are

A $(\sqrt{2}, \sqrt{2})$
B $(\sqrt{2}, 0)$
C $(0, \sqrt{2})$
D $(- \sqrt{2}, 0)$

Verified Solution

Answer & Solution

Correct Answer

(B) $(\sqrt{2}, 0)$

Step-by-step Solution

Detailed explanation

When axes are rotated through an angle θ, then coordinates are X=xcosθ-ysinθ =cos45∘+sin45∘ =12+12=2 Y=xsinθ+ycosθ =sin45∘-cos45∘ =12-12=0 Therefore, the coordinates of P in the original system are (2,0)

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 axes are rotated through an angle 45°, the new coordinates of a point P are (1,-1). The coordinates of P in the original system are

Step-by-step Solution

When the axes are rotated through an angle $45 °$ , the new coordinates of a point $P$ are $(1, - 1)$ . The coordinates of $P$ in the original system are