The equation for the line of reflection which maps the trapezoid onto itself is 
.
Further explanation:
From the given figure it is observed that there is a trapezoid placed vertically and the corner points of the trapezoid are 
and 
.
Label the point 
as A, 
as B, 
as C and as D.
Figure 1 (attached in the end) shows the trapezoid ABCD.
From the given graph it is observed that the length of the side AB is 
, length of side CD is 
.
The line of reflection is a line which reflects the image of an object onto the other side in such a way that the reflected image is same as the original object.
For a regular polygon the line of reflection is the line of symmetry.
This implies that the line of symmetry for the given trapezium is its line of reflection.
A line of symmetry of a figure is a line which divides a figure into exactly two halves such that they can even overlap with each other.
For the given trapezium if we consider the line of symmetry as a vertical line then it is observed that any vertical line which cuts the trapezoid in two parts never gives two symmetrical halves.
From figure 2 (attached in the end) it is observed that any vertical does cut the trapezoid into two symmetrical halves.
The length of the side AB is and the length of the side CD is .
The coordinate of point A is and the coordinate for point B is .
As per the mid-point theorem the mid-point of a line joining the point 
and 
is calculated as follows:
The coordinate of midpoint of AB is calculated as follows:
Therefore, the coordinate of midpoint of AB is 
.
The coordinate of point C is and the coordinate for point D is .
The coordinate of midpoint of CD is calculated as follows:
Therefore, the coordinate of midpoint of CD is 
.
From the above calculation and the given graph it is concluded that the line 
divides the sides AB and CD into two halves.
From figure 3 (attached in the end) it is observed a right angle triangle is formed as 
.
By using the Pythagoras theorem the length of AD is calculated as follows:
Similarly, for 
the length of BC is calculated as follows:
This implies that the sides AD and BC are equal in length.
Since, the length of the side AD and BC are equal so the line will divide the trapezoid into two symmetrical halves in such a way that the two halves completely overlap with each other.
As stated above line of reflection for a regular polygon is its line of symmetry.
This implies that the line is the line of reflection for the trapezoid ABCD.
From figure 4 it is observed that the line is the line of symmetry for the trapezoid ABCD.
Therefore, the equation of line of reflection for the trapezoid is .
Learn more:
1.A problem to complete the square of quadratic function
2.A problem to determine the slope intercept form of a line
3.Inverse function
Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Geometry, coordinate geometry, reflection, symmetry, polygon, line of reflection, line of symmetry, mid-point theorem, trapezoid, map trapezoid onto, equation, y=2, regular polygon, reflection of trapezoid.
