Reflection in the y axis

Have you ever thought about how you would represent the reflection of a point in the y-axis? This is accomplished through the use of reflection in the y-axis concept. If you do not know about it, do not get worried, as this article covers all the concepts of reflection in the y-axis, and the graph xy = 1 is reflected in y = 2x using attractive images so that the children can easily grasp the topics. Let us now begin our learning.

What is the Reflection of a Point in the y-axis?

Reflection of a point in the y-axis states that the y-coordinate stays the same when a point is reflected across the y-axis, the x-coordinate is assumed to be the additive inverse of the given abscissa. For example, a point (x, y) is reflected across the y-axis as (-x, y).

Reflection of a point in the y-axis

A Point on the y-axis has Coordinates  

A point on the y-axis has coordinates in the form of ordered pairs having the form (0, k), where k is the point on the y-axis. Here, 0 specifies the distance between the abscissa and the origin. When x = 0, the value of the y-axis can be anything, irrespective of the value of the abscissa.

Rules to Find the Reflection in the y-axis

There is no hard rule to find the reflection in the y-axis; you just need to follow these two simple steps, which are given below:

1. Keep the coordinates of the y-axis fixed 

2. Reverse the sign of the x coordinate

The obtained value of the x coordinate and y coordinate is the reflection of a point on the y-axis.

Solved Examples

Q 1. Find the reflection of a point on the y-axis of the following:

1. (3, 5)

2. (3, -2)

Ans: For part 1, we need to follow the given steps:

1. Read the coordinates (3, 5) and find out in which quadrant it lies, i.e. 1st quadrant

2. Mark the values of x = 3 and y = 5 in the respective quadrants

3. Highlight the point and write its coordinates

4. To find its reflection, keep the ordinate same, i.e. 5, and take the additive inverse of the abscissa, i.e. -3

5. Now, choose the quadrant for the new coordinates, i.e. (-3, 5)

6. Place the values of x = -3 and y = 5 in the appropriate quadrant

7. Highlight the point and write its coordinates

This is how you find the reflection of a point (3, 5) on the y-axis.

Reflection of a point in the y-axis

For part 2, we need to follow the given steps:

1. Read the coordinates (3, -2) and find out in which quadrant it lies, i.e. 4th quadrant

2. Mark the values of x = 3 and y = -2 in the respective quadrants

3. Highlight the point and write its coordinates

4. To find its reflection, keep the ordinate constant, i.e. -2, and take the additive inverse of the abscissa, i.e. -3

5. Now, choose the quadrant for the new coordinate, i.e. (-3, -2)

6. Mark the values of x = -3 and y = -2 in the appropriate quadrant

7. Highlight the point and write its coordinates

This is how you find the reflection of a point (3, -2) on the y-axis.

Reflection on the y-axis

A point on the y-axis of the following is 5 and -2, respectively, the same as the initial given problem.

Practice Problems 

Q 1. Locate the reflection on the y-axis of the point (5,6).

Ans. (-5, 6)

Q 2. Find the reflection of a point on the y-axis of the following:

(a) (2, -3)

(b) (-3, 7)

Ans. (a) (-2, -3)

(b) (3, 7)

Q 3. Find the reflection on the y-axis of the points:  

(a) (4, 5)

(b) (-1, -2)

Ans. (a) (-4, 5)

(b) (1, -2)

Summary

Summing up here with the concept of reflection in the y-axis. This writing describes all the topics, including rules to find the reflection, graph xy = 1 is reflected in y = 2x, a point on the y-axis has a coordinate, etc. Here we have discussed in depth how to solve the problem based on the reflection of a point in the y-axis. Some practice problems are assigned to the students along with their answers so that they can do more practice and gain proficiency in the concept.