** 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**

RELATED POST