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Byju's Answer

Standard XII

Physics

Displacement of COM:Application

If origin is ...

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

(2, 5)

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(3, 7)

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(4, 9)

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(5, 11)

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Solution

The correct options are
B $(3, 7)$
C $(4, 9)$
Coordinates of P can be
$(\frac{8 + 7}{3}, \frac{16 + 14}{3})$ or $(\frac{14 + 4}{3}, \frac{28 + 8}{3})$ ....(hint: using ratio formula)
=> (15/3, 30/3) or (18/3, 36/3)
$= (5, 10)$ 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 $(4, 9)$

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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

Q. Assertion :

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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

The correct options are B (3,7) C (4,9)Coordinates of P can be (8+73,16+143) or (14+43,28+83) ....(hint: using ratio formula)=> (15/3, 30/3) or (18/3, 36/3)=(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)

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