Shifting of Axes

Q.

If origin is shifted to the point (h, k) the new coordinate of (x, y) will be (x+h, y+k)

1. True

2. False

Q. If $(7,5)$ are the new coordinates of $P$ when origin is shifted to $(1,1)$, then the original coordinates of $P$ are

1. $(8,6)$
2. $(6,4)$
3. $(4,3)$
4. $(-6,-4)$

Q.

The new coordinates of a point (4, 5), when the origin is shifted to the point (1, -2) are

1. (5, 3)

2. (3, 5)

3. (3, 7)

4. (0, 0)

Q. The area of a triangle remains unchanged when the origin is shifted to (h, k).

1. True
2. False

Q. When the origin is shifted to $(1,2),$ the equation $y^2-8x-4y+12=0$ changes to $Y^2=4aX,$ then value of $a$ is

Q. If the origin is shifted to (7, -4), then the coordinates of the point P(4, 5) will become .

1. (-3, 9)
2. (-3, -9)
3. (3, 9)
4. (3, -9)

Q.

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) $e^{\frac{-i\pi }{2}}$

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

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

1. True

2. False

Q.

Without changing the direction of coordinate axes, origin is transferred to (h, k), so that the linear (one degree)

terms in the equation $x^2+y^2-4x+6y-7=0$ are eliminated. Then the point (h, k) is

1. (3, 2)

2. (- 3, 2)

3. (2, - 3)

4. (1.7)

Q. The transformed coordinates of the point $(4,3)$ when the axes are translated to point $(3,1)$ and then rotated through ${30}^{\circ }$ in anticlockwise direction is

1. $(\frac{2\sqrt{3}+1}{2},\frac{\sqrt{3}-2}{2})$
2. $(\frac{\sqrt{3}+1}{2},\frac{2\sqrt{3}+1}{2})$
3. $(\frac{\sqrt{3}+2}{2},\frac{2\sqrt{3}-1}{2})$
4. $(\frac{\sqrt{3}-2}{2},\frac{\sqrt{3}+1}{2})$

Q.

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) $e^{\frac{-i\pi }{2}}$

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

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

1. True

2. False