Reflecting the point (2,-1) about y-axis ,co-ordinate axes are rotated at $45^{\circ}$ angle is negative direction without shifting the origin .after reflection the point is denoted by p and after rotation as q . if the x and y co- ordinates of p and Q are denoted by $x_{p} y_{p}$ and $x_{q} y_{q}$ then, Find new co- ordinates of p

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Solution

This given point is $(2, - 1)$ .
Now, the reflection of point P about y-axis is $P (- 2, - 1)$
Let $(x, y)$ and $(X, Y)$ be the co-ordinates of the point
P referred to old and new axes respectively.
When the axes are rotated through $θ = 45^{\circ}$ , then
$X = x cos θ + y sin θ$
$\Rightarrow x = (- 2) cos 45^{\circ} + (- 1) sin 45^{\circ}$
$X = - 3 / \sqrt{2}$
$Y = - x sin θ + y cos θ = 2 sin 45^{\circ} - 1 cos 45^{\circ} = 1 / \sqrt{2}$
New co-ordinates of P are $(\frac{- 3}{\sqrt{2}}, \frac{1}{\sqrt{2}})$

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