Answer:
see the attachment
Explanation:
You want a graph of the given figure reflected over the line y = 1/3x +1.
Line of reflection
The given line of reflection can be written in general form as ...
y = 1/3x +1
3y = x +3 . . . . . . multiply by 3
x -3y +3 = 0 . . . . subtract 3y
This is in the general form ...
ax +by +c = 0
where a=1, b=-3, c=3.
The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').
Reflected point
Using the formula in the second attachment, we find the reflection
(x1, y1) ⇒ (x, y)
satisfies ...
(x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)
or ...
x = -2a/(a²+b²)·(ax1 +by1 +c) +x1
y = -2b/(a²+b²)·(ax1 +by1 +c) +y1
Using the known values for a, b, c, we have ...
x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1 -3)
y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)
Rewriting the mapping in more conventional terms, we have ...
(x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)
It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).
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Additional comment
The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.