A’B’C’D' will be a reflection of figure ABCD about line f
what is a reflection about a line?
A reflection over a line l(notation l) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line.
reflection of point D will be D' if the distance between point D and line f is the same as the distance between point D' and line f
let us consider point (10,0) on line f for our convenience. we will calculate each distance from this point (10,0)
distance is 2 units from both the points D and D'
reflection of point C will be C' if the distance between point C and line f is the same as the distance between point C' and line f
distance of point C from line f= distance of point C' from line f
[tex]\sqrt{(14-10)^2 + (-2-0)^2} = \sqrt{(10-8)^2+ (4-0)^2} =\sqrt{20}[/tex]
similarly, point A and B will also be equidistant from line f
therefore, A’B’C’D' will be a reflection of figure ABCD about line f.
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