If the origin is shifted to the point (2, -1) by a translation of the axes, the coordinates of a point become (-3, 5). Find the origin coordinates of the point.

Question

Philoid · Accepted Answer

Let the new origin be (h, k) = (2, -1) and (x, y) = (-3, 5) be the given point.

Let the new coordinates be (X, Y)

We use the transformation formula:

x = X + h and y = Y + k

⇒ -3 = X + 2 and 5 = Y + (-1)

⇒ X = -5 and Y = 6

Thus, the new coordinates are (-5, 6)