Question

The coordinates of the point \( (3, -5) \) in the new system, when the origin is shifted to the point \( (-1, -1) \) by the translation of axes, is

• A. \( (4, -4) \)
• B. \( (4, -6) \)
• C. \( (6, -4) \)
• D. \( (4, 4) \)

Hint:

When the origin is shifted from \( (0, 0) \) to \( (h, k) \), the new coordinates \( (x', y') \) of a point with old coordinates \( (x, y) \) are given by \( x' = x - h \) and \( y' = y - k \). Directly apply these formulas with the given old coordinates and the coordinates of the new origin.

Answer 1

The Correct Option is A

Let the coordinates of a point in the old system be \( (x, y) \) and the coordinates of the same point in the new system with the origin shifted to \( (h, k) \) be \( (x', y') \).
The transformation equations are: $$ x = x' + h $$ $$ y = y' + k $$ In this problem, the old coordinates are \( (x, y) = (3, -5) \) and the new origin is \( (h, k) = (-1, -1) \).
We need to find the new coordinates \( (x', y') \).
From the transformation equations, we have: $$ x' = x - h $$ $$ y' = y - k $$ Substituting the given values: $$ x' = 3 - (-1) = 3 + 1 = 4 $$ $$ y' = -5 - (-1) = -5 + 1 = -4 $$ So, the coordinates of the point \( (3, -5) \) in the new system are \( (4, -4) \).