Question

The origin is shifted to (2, 3) by the translation of axes. If the coordinates of a point P change
2.
follows, find the coordinates of P in the original system.
(0) (4,5)
(1) (-4,3)
(iii) (0,0)​

Answer 1

Given : The origin is shifted to (2, 3) by the translation of axes.

coordinates of a point P change to (2 , 2)

To Find :  the coordinates of P in the original system.

Solution:

origin is shifted to (h, k)

Then New coordinates for original  (x , y)

would be (x - h , y - k)

origin is shifted to (2, 3)

h = 2 , k = 3

Let say coordinate of P in original system = ( x , y)

Then in new system =   (x - 2 ,  y - 3)

x - 2 = 2

=> x = 4

y - 3 = 2

=> y = 5

( 4 , 5) are the coordinates of P in the original system.

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Answer 2

Answer:

When the point (x,y) changes to (X,Y) on shifting the origin to (h,k)

Then, x=X+h,y=Y+k

x=2−3,y=3+7

⇒x=−1,y=10

So, the original coordinates are (−1,10)