If the coordinates (x, y) of a point are transformed to (X, Y) when the axes are translated to the point (h,k) then x= x
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In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new coordinate system has coordinates (h, k) in the original system. The positive x' and y'
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2]
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2]
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2]
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2]
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2]
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2] (2)
{\displaystyle x=x'+h} x = x' + h and {\displaystyle y=y'+k} y = y' + k (1)or equivalently{\displaystyle x'=x-h} x' = x - h and {\displaystyle y'=y-k.} y' = y - k .[1][2] (2)In the new coordinate system, the point P will appear to have been translated in the opposite direction. For example, if the xy-system is translated a distance h to the right and a distance k upward, then P will appear to have been translated a distance h to the left and a distance k downward in the x'y'-system . A translation of axes in more than two dimensions is