204

You visited us 204 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Quantitative Aptitude

Lines and Angles

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 ( $α$ , $β$ ) . Find $α$ and $β$ .

Open in App

Solution

Point $B$ is $(2, 1)$
Image of $(2, 1)$ about $X -$ axis $(y = 0)$ is $(2, - 1)$
$∴ α = 2$ and $β = - 1$

Suggest Corrections

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)

, then:

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. A straight line cuts the

x

-axis at point

A (1, 0)

and

y

-axis at point

B

, such that

∠ O A B = α, (α > π / 4)

C

is the middle point of

A B

. If

B^{'}

is the mirror image of

B

with respect to line

O C

and

C^{'}

is a mirror image of point

C

with respect to line

B B^{'}

, then the ratio of the areas of triangle

A B B^{'}

and

B B^{'} C^{'}

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 |

Join BYJU'S Learning Program

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 .

Point B is (2,1) Image of (2,1) about X−axis (y=0) is (2,−1)∴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 ( $α$ , $β$ ) . Find $α$ and $β$ .

Point $B$ is $(2, 1)$
Image of $(2, 1)$ about $X -$ axis $(y = 0)$ is $(2, - 1)$
$∴ α = 2$ and $β = - 1$