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Standard XII

Mathematics

Reflection of a Point about a Line

The image of ...

Question

The image of the point $P (3, 5)$ with respect to the line $y = x$ is the point $Q$ and the image of $Q$ with respect to the line $y = 0$ is the point $R (a, b)$ , then $(a, b)$ is equal to

(5, 3)

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(5, - 3)

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(- 5, 3)

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(- 5, - 3)

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Solution

The correct option is B $(5, - 3)$
The image of the point $P (3, 5)$ w.r.t. the line $y = x$ is $(5, 3)$

$∴$ Coordinates of $Q$ are $(5, 3)$
Taking image w.r.t $y = 0$ , we get
$R \equiv (5, - 3)$

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Similar questions

Q. If the image of the point

P (3, 5)

with respect to the line

y = x

is the point

Q

and the image of

Q

with respect to the line

y = 0

is the point

R (a, b)

, then

(a, b)

is equivalent to

Q. The image of the point

P (3, 5)

with respect to the line

y = x

is the point

Q

and the image of

Q

with respect to the line

y = 0

is the point

R (a, b)

, then

(a, b)

is equal to

Q. The point

P (3, 6)

is first reflected on the line

y = x

and then the image point Q is again reflected on the line

y = - x

to get the image point

Q^{'}

. Then the circumcentre of the

△ P Q Q^{'}

is:

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. The image of the point

(4, - 3)

with respect to the line

y = x

is:

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Reflection of a Point about a Line

Standard XII Mathematics

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The image of the point P(3,5) with respect to the line y=x is the point Q and the image of Q with respect to the line y=0 is the point R(a,b), then (a,b) is equal to

The correct option is B (5,−3)The image of the point P(3,5) w.r.t. the line y=x is (5,3) ∴ Coordinates of Q are (5,3) Taking image w.r.t y=0, we get R≡(5,−3)

The image of the point $P (3, 5)$ with respect to the line $y = x$ is the point $Q$ and the image of $Q$ with respect to the line $y = 0$ is the point $R (a, b)$ , then $(a, b)$ is equal to

The correct option is B $(5, - 3)$
The image of the point $P (3, 5)$ w.r.t. the line $y = x$ is $(5, 3)$

$∴$ Coordinates of $Q$ are $(5, 3)$
Taking image w.r.t $y = 0$ , we get
$R \equiv (5, - 3)$