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Standard X

Mathematics

Reflection in the Origin

The point P 5...

Question

The point P(5, 3) was reflected in the origin to get P'. If M is foot of the perpendicular from P to x -axis & N is foot of the perpendicular from P' to x -axis , Name the figure PMP'N

Rectangle

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Paralleogram

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Rhombus

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Square

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Solution

The correct option is B
Paralleogram

P' is image after reflection of point P(5, 3) of point P (-5, -3)

$P M = \sqrt{(5 - 5)^{2} + (3 - 0)^{2}} = 3$

$P^{'} N = \sqrt{(- 5 - (- 5))^{2} + (- 3, - 0)^{2}} = 3$

$P N = \sqrt{{[5 - (- 5)]}^{2} + (3 - 0)^{2}} = \sqrt{100 + 9} = \sqrt{109}$

$P^{'} M = \sqrt{(- 5 - 5)^{2} + (- 3 - 0)^{2}} = \sqrt{100 + 9} = \sqrt{109}$

Opposite sides are equal and parallel - Hence it is a parallelogram.

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Similar questions

The point P (5, 3) was reflected in the origin to get the image P'.

(a) Write down the co-ordinates of P'.

(b) If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.

(d) Name the figure PMP'N.

(e) Find the area of the figure PMP'N.

Q. Use graph paper for this question. The point

(5, 3)

was reflected in the origin to get the image

P^{'}

.
1. write down the coordinates of

p^{'}

.
2. If M is foot of perpendicular from

p

to x-axis, find the coordinates of

M

.
3. If

N

id the foot of perpendicular from

p^{'}

to the x-axis, find the coordinates of

N

.
4. Name the figure

P M P^{'} N

.
5. Find the area of the area

P M P^{'} N

Q. M is the foot of perpendicular drawn from

P (5, 1)

to the

x

-axis. Then the coordinates of M are

Q. The co-ordinates of the foot perpendicular from P(-3, 1) to X axis are .................

Q. The line x + y = 1 meets x-axis at A and y-axis at B. P is the mid-point of AB.

P_{1}

is the foot of the perpendicular from P to OA;

M_{1}

is that from

P_{1}

to OP;

P_{2}

is that from

M_{1}

to OA; is that from

P_{2}

to OP;

P_{3}

is that from

M_{1}

to OA and so on. If

P_{n}

denotes the nth foot of the perpendicular on OA from

M_{n - 1}

, then

O P_{n}

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