If a point P has coordinates 3-4 in a coordinate system X-OX- Y-OY- and if O has coordinates 4-3 in another system X1-O1X1-Y1-O1Y1 with X-OX-X1-O1X1- then the coordinates of P in the new system X1-O1X1-Y1-O1Y1 is

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Byju's Answer

Standard XII

Mathematics

Equation of a Plane : Intercept Form

If a point ...

Question

If a point $P$ has coordinates $(3, 4)$ in a coordinate system $X^{'} O X \leftrightarrow Y^{'} O Y$ , and if $O$ has coordinates $(4, 3)$ in another system $X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}$ with $X^{'} O X ∥ X_{1}^{'} O_{1} X_{1}$ , then the coordinates of $P$ in the new system $X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}$ is ________________

(3, 4)

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(1, - 1)

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(7, 7)

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(- 1, 1)

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Solution

The correct option is B $(7, 7)$
Given the point P has coordinate (3,4).Similarly O has (4,3)
Given that $X^{'} O X \leftrightarrow Y^{'} O Y X_{1}^{^{'}} O_{1} X_{1} \leftrightarrow Y_{1}^{^{'}} O_{1} Y_{1} ⟹ X^{^{'}} O X ∥ X_{1}^{^{'}} O_{1} X_{1}$
$∴$ Coordinate of P in new system $X_{1}^{^{'}} O X_{1} \leftrightarrow Y_{1}^{^{'}} O Y_{1} = (3 + 4,) = (7, 7)$

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Similar questions

Q. A point

P

has coordinates

(7, 10)

in a coordinate system

X^{'} O X \leftrightarrow Y^{'} O Y

. Suppose it has coordinates

(10, 7)

in another coordinate system

X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}

with

X^{'} O X \leftrightarrow X_{1}^{'} O_{1} X_{1}

. Find the coordinates of

O_{1}

in the system

X^{'} O X \leftrightarrow Y^{'} O Y

Q. Suppose

P

is a point with coordinates

(- 8, 3)

with respect to a coordinate system

X^{'} O X \leftrightarrow Y^{'} O Y

. Let

X_{1}^{^{'}} O_{1} X_{1} \leftrightarrow Y_{1}^{^{'}} O_{1} Y_{1}

be another system with

X^{'} O X ∥ X_{1}^{^{'}} O_{1} X_{1}

and suppose

O_{1}

has coordinates

(9, 5)

with respect to

X^{'} O X \leftrightarrow Y^{'} O Y

. What are the coordinates of

P

in the system

X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}

Q. Suppose

P

has coordinates

(10, 2)

in a coordinate system

X^{'} O X - Y^{'} O Y

and

(- 3, - 6)

in another coordinate system

X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}

with

X^{'} O X ∥ X_{1}^{'} O_{1} X_{1}

. Determine the coordinates of

O

with respect to the system

X_{1}^{'} O_{1} X_{1} \leftrightarrow Y_{1}^{'} O_{1} Y_{1}

Choose the correct option:

If a point P has coordinates (3, 4) in a coordinate system, and if O has coordinates (4, 3) in another systemwith X′OX ||, then the coordinates of P in the new system is _____________.

A. (3, 4)

B. (1, −1)

C. (7, 7)

D. (−1, 1)

Suppose P is a point with coordinates (−8, 3) with respect to a coordinate system X’OX ↔ Y′OY. Let be another system with X′OX || and suppose Q₁ has coordinates (9, 5) with respect to X′OX ↔ Y′OY. What are the coordinates of P in the system?

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If a point P has coordinates (3,4) in a coordinate system X′OX↔Y′OY, and if O has coordinates (4,3) in another system X′1O1X1↔Y′1O1Y1 with X′OX∥X′1O1X1, then the coordinates of P in the new system X′1O1X1↔Y′1O1Y1 is ________________

The correct option is B (7,7)Given the point P has coordinate (3,4).Similarly O has (4,3)Given that X′OX↔Y′OYX′1O1X1↔Y′1O1Y1⟹X′OX∥X′1O1X1∴ Coordinate of P in new system X′1OX1↔Y′1OY1=(3+4,)=(7,7)