Old co-ordinate = $(z, y) = (b, - 2)$
shift of origin = $(h, k) = (- a, p)$
New co-ordinat= $(x, y)$ =

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Solution

We have,

$x = z - h$ $y = y - k$

$x = b - (- a)$ $y = - 2 - p$

$x = a + b$ $y = - (p + 2)$

New coordinate $= (x, y)$ $= (a + b, - (p + 2))$

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Similar questions

Q. Find the co-ordinates of the point, where the origin is shifted, axes remaining parallel, if the old and new co-ordinates of the points are given, in each of the following.

Old co-ordinates
i) (2, 3)
ii) (3, -4)
iii) (a, b)

New co-ordinates
(5, -2}
(7, 2)
(c, d)

In the new coordinate system origin is shifted to (h,k) and the axes are rotated through angle of $90^{\circ}$ in the anti-clockwise direction. The new co-ordinates of (x,y) is obtained by the following method.

1) (x + iy) becomes (x + iy) $e^{\frac{- i π}{2}}$

Let it be (x+iy) or (x,y)

2)(x,y) becomes (x - h,y - k)

Q. If origin is shifted to

(1, 2)

, then old Co-ordinate of

(- 5, - 3)

1) (x + iy) becomes (x + iy) $e^{\frac{- i π}{2}}$

Let it be (x+iy) or (x,y)

2)(x,y) becomes (x - h,y - k)

Q. 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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Old co-ordinate =(z,y)=(b,−2)shift of origin =(h,k)=(−a,p)New co-ordinat=(x,y)=

We have,x=z−h y=y−kx=b−(−a) y=−2−px=a+b y=−(p+2)New coordinate =(x,y) =(a+b,−(p+2))

Old co-ordinate = $(z, y) = (b, - 2)$
shift of origin = $(h, k) = (- a, p)$
New co-ordinat= $(x, y)$ =

We have,

$x = z - h$ $y = y - k$

$x = b - (- a)$ $y = - 2 - p$

$x = a + b$ $y = - (p + 2)$

New coordinate $= (x, y)$ $= (a + b, - (p + 2))$