Question

Find the transformed equation of the straight line 2x – 3y + 5 = 0, when the origin is shifted to the point (3, -1) after translation of axes.

Answer 1

Let coordinates of a point P changes from (x, y) to (X, Y) in new coordinate axes whose origin has the coordinates h = 3, k = -1. Therefore, we can write the transformation formulae as x = X + 3 and y = y – 1.

Substituting, these values in the given equation of the straight line, we get 2(X + 3) – 3 (Y – 1) + 5 = 0 or 2X – 3Y + 14 = 0. Therefore, the equation of the straight line in new system is 2x – 3y + 14 = 0.