Reflection of a Point in x-axis

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

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

Reflection in x-axis

When point M is reflected in x-axis, the image M’ is formed in the fourth quadrant whose co-ordinates are (h, -k). Thus we conclude that when a point is reflected in x-axis, then the x-co-ordinate remains same, but the y-co-ordinate becomes negative.

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

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

(i) Retain the abscissa i.e., x-coordinate.

(ii) Change the sign of ordinate i.e., y-coordinate.


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

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

(i) (-5 , 2)            

(ii) (3, -7)             

(iii) (2, 3)                               

(iv) (-5, -4)

Solution:

(i)The image of (-5 , 2) is (-5 , -2).

(ii) The image of (3, -7) is (3, 7).

(iii) The image of (2, 3) is (2, -3).

(iv) The image of (-5, -4) is (-5, 4).


2. Find the reflection of the following in x-axis:

(i) P (-6, -9)

(ii) Q (5, 7)

(iii) R (-2, 4)

(iv) S (3, -3)

Solution:

The image of P (-6, -9) is P' (-6, 9).

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

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

The image of S (3, -3) is S' (3, 3) .


Solved example to find the reflection of a triangle in x-axis:

3. Draw the image of the triangle PQR in x-axis. The co-ordinate of P, Q and R being P (2, -5); Q (6, -1); R (-4, -3)

Solution:

Reflection of a Point in x-axis

Plot the points P (2, -5); Q (6, -1); R (-4, -3) on the graph paper. Now join PQ, QR and RP; to get a triangle PQR.

When reflected in x-axis, we get P' (2, 5); Q' (6, 1); R' (-4, 3). Now join P'Q', Q'R' and R'P'.

Thus, we get a triangle P'Q'R' as the image of the triangle PQR in x-axis.

Solved example to find the reflection of a line-segment in x-axis:

4. Draw the image of the line segment PQ having its vertices P (-3, 2), Q (2, 7) in x-axis.

Solution:

Reflection of a Line-segment in x-axis

Plot the point at P (-3, 2) and at Q (2, 7) on the graph paper. Now join P and Q to get the line segment PQ.

When reflected in x-axis P (-3, 2) become P' (-3, -2) and Q (2, 7) become Q' (2, -7) on the same graph. Now join P'Q'.

Therefore, P'Q' is the image of PQ when reflected in x-axis.

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

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

  • x-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 fourth 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 y-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 x-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. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More