TS EAMCET · Maths · Straight Lines
The line joining the points \(A(2,0)\) and \(B(3,1)\) is rotated through an angle of \(45^{\circ}\), about \(A\) in the anti-clockwise direction. The coordinates of \(B\) in the new position
- A \((2, \sqrt{2})\)
- B \((\sqrt{2}, 2)\)
- C \((2,2)\)
- D \((\sqrt{2}, \sqrt{2})\)
Answer & Solution
Correct Answer
(A) \((2, \sqrt{2})\)
Step-by-step Solution
Detailed explanation
Slope of \(A B=\frac{1-0}{3-2}=1\) Therefore, \(\angle B A X=45^{\circ}\) But \(\angle B A C=45^{\circ}\) \(\angle C A X=90^{\circ}\) So, the equation of \(A C\) is \(\frac{x-2}{\cos 90^{\circ}}=\frac{y-9}{\sin 90^{\circ}}=r \text { (say) }\) We have…
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