Question

If the origin is shifted to the centre of the rectangle with vertices $(0,0)$, $(6,0)$, $(6,4)$ and $(0,4)$ without rotation of axes, then the coordinates of vertices of the rectangle with respect to the new system of coordinates is

• A. $(-3,-2)$
• B. $(3,-2)$
• C. $(3,2)$
• D. $(-3,2)$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $(3,-2)$
B $(3,2)$
C $(-3,2)$
D $(-3,-2)$

Let the rectangle be ABCD where $A(0,0),B(6,0),C(6,4),D(0,4)$

Centre of the rectangle can be found by taking the mid-point of the diagonals,

Suppose we take BD diagonal then mid point of BD is $(\frac{0+6}{2},\frac{4+0}{2})$ which is $3,2$

Centre of the rectangle is $(3,2)$, coordinates of the vertices in the new system of coordinates are $(-3,-2)$, $(6-3,-2)$, $(6-3,4-2)$ and $(-3,4-2)$ i.e. $(-3,-2)$, $(3,-2)$, $(3,2)$ and $(-3,2)$