In this chapter we will learn the concept of reflection across the x axis with solved examples.
Let us first review the basics of reflection.
What is Reflection ?
The formation of mirror image of any body is called reflection.
The reflected image has following property;
(a) it is flipped in orientation
(b) it has same size and dimensions
(c) it is located in opposite direction of original object
Reflection of point across x axis
In this concept, the x axis of the cartesian place act as a mirror.
So when we place a point around x axis, we get reflected image on the other side of the axis.
Note that the distance of reflected image from the x axis is same as the distance of original image.
For example, consider the below image.
Note that;
⟹ Original image lies at (-2, 1)
⟹ Red line is X axis which act as mirror
⟹ Reflected image is at (-2, -1)
Both the original & reflected image is equidistant from the central mirror axis.
Shortcut rules for reflection of point over x axis
The following shortcut rules will help you to find the reflection of point along x axis.
To locate the reflected point location;
(a) retain the x coordinate of original point
(b) change the sign of y coordinate of original point
After following the above steps, you will get the located of reflected image of the point.
Let us understand the above rules with examples;
Example 01
The point (3, 5) is reflected along x axis. Locate the position of reflected image.
Solution
Following the above rules, if the point is reflected along x axis then;
⟹ Retain the position of x coordinate
⟹ change the sign of y coordinate
Hence the location of reflected point is ( 3, -5)
Given below is the position of image in graphical form.
In the above image;
⟹ Original Point ( 3, 5 )
⟹ Red line is x axis which is mirror
⟹ Reflected Image ( 3, -5)
Example 02
The point (-3, -2) is reflected along x axis. Locate the position of reflected image.
Solution
Since the point is reflected along x axis, the reflected image contain:
⟹ same x coordinate
⟹ y coordinate with different sign.
Hence, the location of reflected image is (-3, 2)
Plotting the images in graph diagram.
In the above image;
⟹ Original Point ( -2, -3 )
⟹ Red line is x axis which is mirror
⟹ Reflected Image ( -2, 3)
Reflection of Image across x axis
You can also use above mentioned rules to draw the reflected image of simple geometrical figure.
Given below is the example of plotting reflected image of triangle along x axis.
The above image contains triangle with coordinates A (-4, 3), B (-4, 1) and C (-2, 1).
Now use the above mentioned x axis mirror rule to identify the position of reflected points.
The rule says to retain the x coordinate and change the sign of y coordinate.
⟹ (-4, 3) reflected image is (-4, -3)
⟹ (-4, 1) reflected image is (-4, -1)
⟹ (-2, 1) reflected image is (-2, -1)
Plotting the reflected points in cartesian graph, we get;
Join all the points and we will get the reflected image.
