Point (-1, 2) is changed to (a, b) when the o | vedclass

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(C) Step $1$: Translation of axes.Given original point $(x, y) = (-1, 2)$ and new origin $(h, k) = (2, -1)$.The new coordinates $(a, b)$ are given by

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$(3\sqrt{2}, 0)$

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(C) Step $1$: Translation of axes.Given original point $(x, y) = (-1, 2)$ and new origin $(h, k) = (2, -1)$.The new coordinates $(a, b)$ are given by $a = x - h = -1 - 2 = -3$ and $b = y - k = 2 - (-1) = 3$.So,$(a, b) = (-3, 3)$.Step $2$: Rotation of axes.The axes are rotated by $	heta = 45^{\circ}$ about the new origin $(2, -1)$.The new coordinates $(c, d)$ are given by:$c = a \cos 	heta + b \sin 	heta = -3 \cos 45^{\circ} + 3 \sin 45^{\circ} = -3(\frac{1}{\sqrt{2}}) + 3(\frac{1}{\sqrt{2}}) = 0$.$d = -a \sin 	heta + b \cos 	heta = -(-3) \sin 45^{\circ} + 3 \cos 45^{\circ} = 3(\frac{1}{\sqrt{2}}) + 3(\frac{1}{\sqrt{2}}) = \frac{6}{\sqrt{2}} = 3\sqrt{2}$.So,$(c, d) = (0, 3\sqrt{2})$.Step $3$: Reflection about $y = x$.The reflection of a point $(x, y)$ about the line $y = x$ is $(y, x)$.Therefore,the reflection of $(0, 3\sqrt{2})$ is $(3\sqrt{2}, 0)$.Thus,$(e, f) = (3\sqrt{2}, 0)$.

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