Translation of axis new axis:Translation of axis, new axis, suppose that x y coordinate be a given and O’ (h, k) be any point in the plane. Though O’ draw two mutually perpendicular lines O’X, O’Y such that O’X is parallel to Ox.
The new axis O’X and O’Y are called TRANSLATION of the Ox- and O y-axis through the point O’.
In translation of axis, the origin is shifted to another point in the plane, but the axis remains parallel to the old axis.
XY- coordinate system referred
Let p be a point with coordinates (x, y) referred to x y-coordinate system and the axis be translated through the point O'(h, k) and O’X, O’Y be a new Axis. If P has coordinated (X, Y) suffered to the new Axis then we need to fined X, Y in terms of x, y
Draw PM and O’N perpendiculars to Ox.
From the figure, we have
OM= x, MP=y, ON= h, NO’= k= MM’
NOW
X = O’M’ = NM= OM-ON = x-h
Similarly,
Y = M’P = MP – MM’ = y-k
Thus, the coordinate of referred to XY- system are (x-h, y-k)
That is,
X = x – h
Y = y – k
Moreover,
x = X + h,
y = Y + k
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