The line segment joining A(3, 0), B(5, 2) is rotated about a point A in anticlockwise sense through an angle π4 and B move to C. If a point D be the reflection of C in y-axis, then D=

AB=r=22,θ=450+450=90∘ using x=x1+rcos⁡θ,y=y1+rsin⁡θwe get C=(3,22)∴D= reflection of C(3,22) in Y-axis =(−3,22)

The line segment joining A(3, 0), B(5, 2) is rotated about a point A in anticlockwise sense through an angle π4 and B move to C. If a point D be the reflection of C in y-axis, then D=

AB=r=22,θ=450+450=90∘ using x=x1+rcos⁡θ,y=y1+rsin⁡θwe get C=(3,22)∴D= reflection of C(3,22) in Y-axis =(−3,22)

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The line segment joining A(3, 0), B(5, 2) is rotated about a point A in anticlockwise sense through an angle $\frac{π}{4}$ and B move to C. If a point D be the reflection of C in y-axis, then D=

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$(- 3, 2 \sqrt{2})$

$(3, 2 \sqrt{2})$

$(3, - 2 \sqrt{2})$

$(3, 8 \sqrt{2})$

answer is A.

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$\begin{aligned} A B = r = 2 \sqrt{2}, θ = 45^{0} + 45^{0} = 90^{\circ} \\ using x = x_{1} + r \cos θ, y = y_{1} + r \sin θ \end{aligned}$
we get $C = (3, 2 \sqrt{2})$
$∴ D = reflection of C (3, 2 \sqrt{2}) in Y-axis = (- 3, 2 \sqrt{2})$

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The line segment joining A(3, 0), B(5, 2) is rotated about a point A in anticlockwise sense through an angle π4 and B move to C. If a point D be the reflection of C in y-axis, then D=

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The line segment joining A(3, 0), B(5, 2) is rotated about a point A in anticlockwise sense through an angle $\frac{π}{4}$ and B move to C. If a point D be the reflection of C in y-axis, then D=