Question

If the origin is shifted to the point (2, 3), the coordinates of a point become (5, -4). Find the original coordinates, when the axes are parallel.

Answer 1

Let the original coordinates be P(x, y).

Let the origin O be shifted to the new point O' (h, k), where h = 2 and k = 3.

Then, the new coordinates of P are (x', y'), where x' = 5 and y' = -4.

Now, x' = x-h $\Rightarrow$ 5 = x - 2 $\Rightarrow$ x = 7.

And, y' = y- k $\Rightarrow$-4= y-3 $\Rightarrow$ y = -1 Hence, the original coordinates are (7, -1)