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Transformations of Axes - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 4 Questions around this concept.

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Point \mathrm{P(a, b)}  lie on the line \mathrm{y=x+1 . P} is shifted in the direction perpendicular to the given line so that it meets \mathrm{x}-axis at \mathrm{(\alpha, 0)}, then

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Transformations of Axes

Transformations of Axes

Shifting of Origin

Point P has coordinate (x, y) in the original coordinate system, i.e. in xy-coordinate system.

If the new origin takes position as O’(h, k) with new x and y axes remaining parallel to old axes.

The coordinates of the point P are now (X, Y) = (x - h, y - k) w.r.t. the new coordinate system (i.e. Y’O’X’).

Thus,  X = x - h  and  Y = y - k

Or, x = X + h  and  y = Y + k

Note: 

If the function f(x, y) = 0 is with respect to original coordinate system, then the equation with respect to new coordinate system is f(x + h, y + k) = 0.

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