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If a point is shifted to the right, the new x co-ordinate is given by adding the shift to the old x co-ordinate. If a point is shifted to the left, the new x co-ordinate is given by subtracting the shift from the old x co-ordinate.

Reflection of a point

When you stand in front of a mirror your reflection is located the same distance ( d ) behind the mirror as you are standing in front of the mirror.

We can apply the same idea to a point that is reflected on the x -axis, the y -axis and the line y = x .

Reflection on the x -axis

If a point is reflected on the x -axis, then the reflection must be the same distance below the x -axis as the point is above the x -axis and vice-versa, as though it were a mirror image.

Points A and B are reflected on the x -axis. The original points are shown with and the reflected points are shown with .
When a point is reflected about the x -axis, only the y co-ordinate of the point changes.

Find the co-ordinates of the reflection of the point P, if P is reflected on the x -axis. The co-ordinates of P are (5;10).

  1. We are given the point P with co-ordinates (5;10) and need to find the co-ordinates of the point if it is reflected on the x -axis.

  2. The point P is above the x -axis, therefore its reflection will be the same distance below the x -axis as the point P is above the x -axis. Therefore, y =-10.

    For a reflection on the x -axis, the x co-ordinate remains unchanged. Therefore, x =5.

  3. The co-ordinates of the reflected point are (5;-10).

Reflection on the y -axis

If a point is reflected on the y -axis, then the reflection must be the same distance to the left of the y -axis as the point is to the right of the y -axis and vice-versa.

Points A and B are reflected on the y -axis. The original points are shown with and the reflected points are shown with .
When a point is reflected on the y -axis, only the x co-ordinate of the point changes. The y co-ordinate remains unchanged.

Find the co-ordinates of the reflection of the point Q, if Q is reflected on the y -axis. The co-ordinates of Q are (15;5).

  1. We are given the point Q with co-ordinates (15;5) and need to find the co-ordinates of the point if it is reflected on the y -axis.

  2. The point Q is to the right of the y -axis, therefore its reflection will be the same distance to the left of the y -axis as the point Q is to the right of the y -axis. Therefore, x =-15.

    For a reflection on the y -axis, the y co-ordinate remains unchanged. Therefore, y =5.

  3. The co-ordinates of the reflected point are (-15;5).

Reflection on the line y = x

The final type of reflection you will learn about is the reflection of a point on the line y = x .

Casestudy : reflection of a point on the line y = x

Study the information given and complete the following table:

Point Reflection
A (2;1) (1;2)
B (- 1 1 2 ;-2) (-2;-1 1 2 )
C (-1;1)
D (2;-3)

What can you deduce about the co-ordinates of points that are reflected about the line y = x ?

Questions & Answers

distinguish between anatomy and physiology
Amina Reply
Anatomy is the study of internal structure of an organism while physiology is the study of the function/relationship of the body organs working together as a system in an organism.
adeyeye
distinguish between anatomy and physiology
Erny Reply
regional anatomy is the study of the body regionally
Ismail Reply
what is the meaning of regional anatomy
Aminat Reply
epithelial tissue: it covers the Hollow organs and body cavities
Esomchi Reply
in short way what those epithelial tissue mean
Zainab Reply
in short way what those epithelial tissue mean
Chizoba
What is the function of the skeleton
Lilias Reply
movement
Ogar
Locomotion
Ojo
support
Aishat
and body shape/form
Aishat
what is homeostasis?
Samuel Reply
what's physiology
AminchiSunday Reply
what is physiology
AminchiSunday
physically is the study of the function of the body
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that is what I want ask
YAU
u are wright
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pls what are the main treatment of hiccups
YAU
physiology is the study of the function of the body
Najaatu
hiccups happen when something irritates the nerves that course your diaphragm to contract
Najaatu
how did hypothalamus manege to control all activities of the various hormones
malual
what is protein
Abdulsalam
how can I treat pain a patient feels after eating meals
Namuli Reply
how do I treat a three year old baby of skin infection?
Okocha Reply
It depends on the type of infection. Bacterial, fungal, parasitic or viral?
schler
if you can share the sign ad symptoms of the skin infection then u geh the treatment cox they're different sign ad symptoms of skin infection with different treatment
Sa
the sign and symptoms of maleria
Abdulsalam
prostaglandin and fever
Maha Reply
yes
rayyanu
welcome sir
rayyanu
prostaglandin E2 is the final mediator.
Lemlem
prostaglandin E2 is the final mediator of fever.
Lemlem
yes
Agabi
good evening
Jediel
tissue.
Akoi
explain
Chizoba
Hi
Anya
,good evening
Anya
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
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omeprazole
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Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
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to transport fluids fats proteins and lymphocytes to the blood stream as lymph
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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