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Lines and Angles

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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 $β$ .

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Solution

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

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Q. Assertion :Reflections of the point

(- 3, 2)

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x + y = 0

(- 2, 3) .

Reason: The reflection of a point

P (α, β)

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a x + b y + c = 0

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

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Q. Assertion :Reflection of the point

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a x + b y + c = 0

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Q. Let

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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) . 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 $β = - 1$