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.

Options

• 3X – 2Y + 14 = 0

• 3X – 2Y – 14 = 0

• 2X – 3Y + 14 = 0

• 2X – 3Y – 14 = 0

Answer 1

2X – 3Y + 14 = 0

Explanation:

Let coordinates changes from (x, y) `rightarrow` (X, Y) in new coordinate system whose origin is h = 3, k = –1

∴ x = X + 3, y = Y – 1

So, 2x – 3y + 5 = 0

`\implies` 2 (X + 3) – 3 (Y – 1) + 5 = 0

`\implies` 2X + 6 – 3Y + 3 + 5 = 0

`\implies` 2X – 3Y + 14 = 0