Reflection of a Point in y-axis

How to find the co-ordinates of the reflection of a point in y-axis?

To find the co-ordinates in the adjoining figure, y-axis represents the plane mirror. M is the any point whose co-ordinates are (h, k) in the rectangular axes in first quadrant.

Reflection in y-axis

Observe when point M is reflected in y-axis, the image M' is formed in the second quadrant whose co-ordinates are (-h, k).

Thus we conclude that when a point is reflected in y-axis, then the y-co-ordinate remains same and then x-co-ordinate become negative.

Thus, the image of M (h, k) is M' (-h, k).


Rules to find the reflection of a point in the y-axis:

(i) Change the sign of abscissa i.e., x-coordinate.

(ii) Retain the ordinate i.e., y-coordinate.


Examples to find the co-ordinates of the reflection of a point in y-axis:

1. Write the co-ordinates of the image of the following points when reflected in y-axis.

(i) (-4 , 3)            

(ii) (3, 5)             

(iii) (-1, -6)                               

(iv) (5, -7)

Solution:

(i) The image of (-4 , 3) is (4 , 3).

(ii) The image of (3, 5) is (-3, 5).

(iii) The image of (-1 , -6) is (1, -6).

(iv) The image of (5, -7) is (-5, -7).


2. Find the reflection of the following in y-axis.

(i) P (-7, 9)

(ii) Q (-3, -6)

(iii) R (4, 8)

(iv) S (5, -7)

Solution:

(i) The image of P (-7, 9) is P' (7, 9).

(ii) The image of Q (-3, -6) is Q' (3, -6).

(iii) The image of R (4, 8) is R' (-4, 8).

(iv) The image of S (5, -7) is S' (-5, -7).



Solved example to find the reflection of a parallelogram in y-axis:

3. Draw the image of the parallelogram PQRS having its vertices P (-2, 5); Q (-2, -1); R (-5, -4); S (-5, 2) in y-axis.

Solution:

Reflection of a Point in y-axis

Plot the points P (-2, 5); Q (-2, -1); R (-5, -4); S (-5, 2) on the graph paper. Now join PQ, QR, RS and SP to get a parallelogram.

When reflected in y-axis, we get P' (2, 5); Q' (2, -1); R' (5, -4); S' (5, 2). Now join P'Q', Q'R', R'S' and S'P'.

Thus we get the parallelogram P'Q'R'S as the image of the parallelogram  PQRS in y-axis.


Solved example to find the reflection of a rectangle in y-axis:

4. The co-ordinate of the rectangle PQRS having its vertices P (-4, 5), Q (-1, 5), R (-1, -2), S (-4, -2). Draw the image of the figure when reflected in y-axis.

Solution:

Reflection of a Rectangle in y-axis

Plot the co-ordinates of the points  P (-4, 5), Q (-1, 5), R (-1, -2), S (-4, -2) on the graph paper.

Join PQ, QR, RS and SP to get a rectangle.

When reflected in y-axis we get;

The image of P (-4, 5) is P' (4, 5)

The image of Q (-1, 5) is Q' (1, 5)

The image of R (-1, -2) is R' (1, -2)

The image of S (-4, -2) is R' (4, -2)

Plot the point P', Q', R' and S' on the same graph paper. Now join P'Q', Q'R', R'S' and S'P'.

Thus we get the rectangle P'Q'R'S as the image of the rectangle PQRS when reflection in y-axis.

Note: Point M (h, k) has its image M' (-h, k) when reflected in y-axis.

Thus, we conclude that when the reflection of a point in y-axis:

  • y-axis acts as a plane mirror.
  • M is the point whose co-ordinates are (h, k).
  • The image of M i.e. M' lies in second quadrant.
  • The co-ordinates of M' are (-h, k).


Related Concepts

Lines of Symmetry

Point Symmetry

Rotational Symmetry

Order of Rotational Symmetry

Types of Symmetry

Reflection

Reflection of a Point in x-axis

Reflection of a point in origin

Rotation

90 Degree Clockwise Rotation

90 Degree Anticlockwise Rotation

180 Degree Rotation


7th Grade Math Problems

8th Grade Math Practice

From Reflection of a Point in y-axis to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition

    Apr 24, 25 01:45 AM

    Addition of Decimals
    We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some

    Read More

  2. Addition of Like Fractions | Examples | Videos | Worksheet | Fractions

    Apr 23, 25 09:23 AM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  3. Subtraction | How to Subtract 2-digit, 3-digit, 4-digit Numbers?|Steps

    Apr 23, 25 12:41 AM

    Subtraction Example
    The answer of a subtraction sum is called DIFFERENCE. How to subtract 2-digit numbers? Steps are shown to subtract 2-digit numbers.

    Read More

  4. Subtraction of 4-Digit Numbers | Subtract Numbers with Four Digit

    Apr 23, 25 12:38 AM

    Properties of Subtraction of 4-Digit Numbers
    We will learn about the subtraction of 4-digit numbers (without borrowing and with borrowing). We know when one number is subtracted from another number the result obtained is called the difference.

    Read More

  5. Subtraction with Regrouping | 4-Digit, 5-Digit and 6-Digit Subtraction

    Apr 23, 25 12:34 AM

     Subtraction of 5-Digit Numbers with Regrouping
    We will learn subtraction 4-digit, 5-digit and 6-digit numbers with regrouping. Subtraction of 4-digit numbers can be done in the same way as we do subtraction of smaller numbers. We first arrange the…

    Read More