TS EAMCET · Maths · Straight Lines
The point \(\mathrm{P}(\alpha, \beta)(\alpha>0, \beta>0)\) undergoes the following transformations successively.
a) Translation to a distance of 3 units in positive direction of \(x\)-axis.
b) Reflection about the line \(y=-x\).
c) Rotation of axes through an angle of \(\frac{\pi}{4}\) about the origin in the positive direction.
If the final position of that point P is \((-4 \sqrt{2},-2 \sqrt{2})\), then \((\alpha+\beta)=\)
- A \(5\)
- B \(7\)
- C \(6 \sqrt{2}\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
Given \(P(\alpha, \beta)\) a) Translation: \(P_1 = (\alpha+3, \beta)\) b) Reflection about \(y=-x\): \(P_2 = (-\beta, -(\alpha+3))\) c) Rotation of axes by \(\frac{\pi}{4}\): Final point \((x_f, y_f)\) from \((x,y)\) is \(x_f = x \cos\theta + y \sin\theta\),…
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