Translation of Axes [Definition and Meaning]

Translation of Axes: Let xy-coordinate system be given and O'( h,k) be any point in the plane. Through O' draw two mutually perpendicular lines O'X, O'Y such that O'X is parallel to Ox . The new axes O'X and O'Y are called translation of the Ox and Oy axes through the point O' . In this, the origin is shifted to another point in the plane but the axis remains parallel to the old axes. Let P be a point with coordinates (x,y ) referred to xy -coordinate system and the axes be translated through the point O'(h ,k ) and O'X, O'Y be the new axes. If P has coordinates (X, Y) referred to the new axes, then we need to find X, Y in terms of x, y.

Translation of Axes

Draw PM and O' N perpendiculars to Ox .

From the figure, we have

OM =x,\;\;\;\;\;MP= y,\;\;\;\;\;ON= h,\;\;\;\;\;NO'= k =MM' .


X =O'M' =NM= OM -OM- ON =x -h.


Y =M' P =MP- MM'= y -k

Thus the coordinates of P referred to XY-system are (x-h,y-k ).


X= x-h

Y= y-k .


\boxed{x= X+ h \;\;\;\;and\;\;\;\; y=Y+k}

Example 1:(Translation of Axes)

The coordinates of a point P are (-6, 9). The axes are translated through the point O' (-3, 2). Find the coordinates of Preferred to the new axes.


h=-3\;\;\; and\;\;\;\; k= 2

Coordinates of P referred to the new axes are (X, Y) given by

X =x-h= -6 - (-3) = -3


Y =y-k= 9 - 2 = 7


\boxed{P (X, Y) = P (-3 ,7)}.

Example 2: (Translation of Axes)

The xy -coordinate axes are translated through the point O' (4, 6). The coordinates of the point P are (2, -3) referred to as the new axes. Find the coordinates of Preferred to the original axes.


X=2, \;\;,Y=-3\;,\;h=4 ,\;\;k =6 .

We have

x=X+h = 4+2= 6

y=Y+k = -3+6=3

Thus required coordinates are \boxed{P (6, 3)}

Wikipedia. Do you want to read the geometry topic click here

Spread the love
Azhar Ali

Azhar Ali

I graduated in Mathematics from the University of Sargodha, having master degree in Mathematics.

Leave a Reply

Your email address will not be published.

Mathematics is generally known as Math in US and Maths in the UK.

Contact Us

Copyright by Double Math. All Right Reserved 2019 to 2022