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Standard X

Mathematics

Reflection in the Origin

The image of ...

Question

The image of the point $A (1, 2)$ by the line mirror $y = x$ is the point $B$ and the image of $B$ by the line mirror $y = 0$ is the point $(α, β)$ , then:

α = 1, β = - 2

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α = 0, β = 0

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α = 2, β = - 1

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none of these

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Solution

The correct option is C $α = 2, β = - 1$
If image of $A (1, 2)$ w.r.t line mirror $y = x$ is $B (x_{1}, y_{1})$
then, $x_{1} = 2$ and $y = 1$
and image of $B (2, 1)$ w.r.t x-axis is $(- 2, 1)$
Here, $α = 2$ and $β = - 1$

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Similar questions

Q. The image of the point

A (1, 2)

by the line mirror

y = x

is the point

B

and the image of

B

by the line mirror

y = 0

is the point

(α, β)

. Find

α

and

β

Q. Assertion :Reflections of the point

(- 3, 2)

in the line

x + y = 0

(- 2, 3) .

Reason: The reflection of a point

P (α, β)

in the line

a x + b y + c = 0

is the point

Q (α^{'}, β^{'})

(\frac{α + α^{'}}{2}, \frac{β + β^{'}}{2})

lies on the line.

Q. Assertion :Reflection of the point

(- 3, 2)

in the line

x + y = 0

(- 2, 3)

Reason: The reflection of a point

P (α, β)

in the line

a x + b y + c = 0

is the point

Q (α^{'}, β^{'})

, if

(\frac{α + α^{'}}{2}, \frac{β + β^{'}}{2})

lies on the line.

Q. Reflection of the point

(α, β, γ)

X Y

plane is

Q. Let

P_{1} : x + y + z = 0

P_{2} : x + 2 y + 3 z = 0

P_{3} : x + 3 y + 5 z = 0

be three planes

L_{1}

is the line of intersection of

P_{1}

P_{2} . Let P (2, 1, - 1)

be point on

P_{3}

. If

(α, β, γ)

is image of point

P

in the line

L_{1}

then the value of

| α + β + γ |

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The image of the point A(1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point (α,β), then:

The correct option is C α=2,β=−1If image of A(1,2) w.r.t line mirror y=x is B(x1,y1)then, x1=2 and y=1and image of B(2,1) w.r.t x-axis is (−2,1)Here, α=2 and β=−1

The image of the point $A (1, 2)$ by the line mirror $y = x$ is the point $B$ and the image of $B$ by the line mirror $y = 0$ is the point $(α, β)$ , then:

The correct option is C $α = 2, β = - 1$
If image of $A (1, 2)$ w.r.t line mirror $y = x$ is $B (x_{1}, y_{1})$
then, $x_{1} = 2$ and $y = 1$
and image of $B (2, 1)$ w.r.t x-axis is $(- 2, 1)$
Here, $α = 2$ and $β = - 1$