In this article, we will explain in detail the reflection of a point in a line parallel to the x-axis by taking an example. We will show how to plot the points on the graph to know the reflection of a point in the x-axis. The y-coordinate of each point on the line parallel to the x-axis is constant i.e., remain the same.
Also Read:
- Reflection of a Point in the y-axis
- Reflection of a point in the x-axis
- Reflection of a Point in the Origin
What is Reflection of a Point in a Line along the x-axis?
Let P be the point on the x-axis with the coordinates (x, y). Let the image of P be P’ in the horizontal line drawn on the x-axis. The image of the point (x, y) in the line parallel to the x-axis. When it comes to the refection of a point in a line parallel to the x-axis the sign of the x-axis will be changed and the sign of the y-axis remains the same.
Reflection of a Point in a Line Parallel to the x-axis Examples
Let us discuss the concept of Reflection of a Point in a Line Parallel to the x-axis with some examples.
Example 1.
Point P (a, b) is reflected in the x-axis to P’ (-5, 3). Write down the values of a and b.
Solution:
Given points are (-5, 3)
We know Mx (x, y) = (x, -y)
P'(-5, 3) = reflection of P (a, b) in x-axis.
Thus, the coordinates of P are (5, 3).
Hence, a = 5 and b = 3
Example 2.
Find the Reflection of the point (-5,7).
Solution:
Given that the point is (-5,7)
When a point is reflected in the x-axis, the sign of its ordinate changes.
Reflection of the point
(-5,7) in the x-axis is (5,7).
Example 3.
The image of a point P reflected in the x-axis is (-4,4). Find the coordinates of P.
Solution:
Given that the point is P(-4,4)
When a point is reflected in the x-axis, the sign of its ordinate changes. Hence, the coordinates of P are (4,4)
Example 4.
A point P is reflected in the x-axis. Coordinates of its image are (-3,9). Find the coordinates of the image of P under reflection in the x-axis.
Solution:
Given that the point is P(-3,9)
The Coordinates of the image of P are under reflection in the x-axis (3,9).
Example 5.
Find the Reflection of the point (-3,8).
Solution:
Given that the point is (-3,8)
When a point is reflected in the x-axis, the sign of its ordinate changes.
Reflection of the point
(-3,8) in the x-axis is (3,8).
FAQs on Reflection of a Point in a Line Parallel to the x-axis
1. What does it mean if a point is parallel to the x-axis?
The point Parallel to the axis means the lines that are parallel to either the x-axis or y-axis.
A line parallel to the x-axis is called the horizontal line.
The equation is in the form of y = k, where ‘k’ is the distance of the line from the x-axis.
2. What is the rule for reflecting a point across the x-axis?
The rule for a reflection of the x -axis is (x,y) = (x,−y).
3. What is the image of a point after a reflection in the x-axis?
The point M is reflected in the x-axis the image M’ is formed in the fourth quadrant and their coordinates are (h, -k). Hence the point is reflected in the x-axis the x-coordinate remains the same, but the y-coordinate becomes negative. Thus, the image of point M (h, k) is M’ (h, -k).