Question

Find the new coordinates of the point $(1, 1)$ if the origin is shifted to the point $(-3, -2)$ by a translation of axes.

• A. $(4,3)$
• B. $(3,3)$
• C. $(5,3)$
• D. $(5,4)$

Answer 1

Answer: (A)

$(4,3)$

Answer 2

The coordinates of new origin are $h = - 3$, $k =-2$ and original coordinates are given by $x = 1$, $y = 1$. The transformation relation between the old coordinates $(x, y)$ and the new coordinates $(x', y')$ are given by $x = x' + h$ $\Rightarrow x'=x-h$ $y = y' +k$ $\Rightarrow y' =y-k$ Substituting the values, we have $x'= 1 + 3 = 4$, $y' = 1 + 2 =3$ Hence, the coordinates of the point $(1, 1)$ in the new system are $(4,3)$.