Question

If origin is shifted to the point $(2,3)$ without rotation of axes then the coordinates of the point $P$ which divides the join of $A(4,8)$ and $B(7,14)$ in the ratio $1:2$ or $2:1$ with respect to the new system of coordinates can be

• A. $(2,5)$
• B. $(3,7)$
• C. $(4,9)$
• D. $(5,11)$

Answer 1

Answer: (B), (C)

The correct options are
B

$(3,7)$

C

$(4,9)$

Coordinates of P can be
$(\frac{8+7}{3},\frac{16+14}{3})$ or $(\frac{14+4}{3},\frac{28+8}{3})$
$=(5,10)$ or $(6,12)$ in old system of coordinates.
$=(5-2,10-3)$ or $(6-2,12-3)$ in new system of coordinates $=(3,7)$ or $(4,9)$