Question

# In the new coordinate system origin is shifted to (h,k) and the axes are rotated through angle of 90∘ 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−iπ2 Let it be (x+iy) or (x,y) 2)(x,y) becomes (x - h,y - k)

A

True

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B

False

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Solution

## The correct option is B False We know when the origin gets shifted to (h,k) the new coordinates of (x,y) will be (x-h,y-k).we also know when we rotate the coordinate axes through an angle of (x+iy) becomes (x+iy)−iθ, because it is equivalent to rotating through -θ We can do it in both ways, first rotation then translation and vice versa.But after we rotate the coordinate axes, the coordinates of the origin also changes.We did not account for that in the question.We should not subtract (h,k) from (x,y).

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