What is the equation for the line of reflection that maps the trapezoid onto itself?
1 Answer
The equation of line of reflection is
Explanation:
It is apparent that we can have a line of reflection that maps a trapezoid onto itself,
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only when the trapezoid has the two non-parallel sides are equal in length and angles they make with any of the parallel sides too are equal (in fact the first condition in a trapezium leads to second) i.e. an isosceles trapezoid. Here, it is so and hence we have a line of reflection that maps a trapezoid onto itself.
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Further such a line of reflection would be perpendicular to the parallel sides and as here parallel sides are parallel to
#x# -axis, the line of reflection would be parallel to#y# axis i.e. of the form#x=a# -
Further as every point and its reflection is equidistant from the line of reflection, the line of reflection must pass through the midpoints of parallel sides.
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In the given figure, mid points of parallel sides are
#(2,2)# and#(2,6)#
Hence the equation of line of reflection is
