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Geometry

Isometries

Reflection

         

The lengths of the lines in the above figure (a half house) are as follows: \[\lvert \overline{AB} \rvert = 9, \lvert \overline{BC} \rvert = 3,\]\[ \lvert \overline{CD} \rvert = 3, \lvert \overline{DE} \rvert = 3, \lvert \overline{EA} \rvert = 12.\] If the shape is flipped across the line segment \(\overline{AE}\) to complete a house, what will be the perimeter of the house?

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The reflection of the circle \(x^2+y^2-20x-20y+196=0\) in the origin \((0,0)\ \) is \(\ x^2+y^2+ax+by+c=0.\) What is \(a+b+c\)?

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The point \(A=(-4,5)\) is reflected in the line \(y=x.\) What are the coordinates of the resulting image?

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If rectangle \(ABCD\) in the above graph is reflected in the line \(y = -1,\) what is the image of point \(D?\) The side length of each square in the graph paper is \(1.\)

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In the above diagram, shape \(B\) on the right is the reflection of shape \(A\) in the red line. Given the following numbers: \[L = 48, \quad N = 3, \quad M = 6\] in the diagram, what is the value of \(a - b + c - d?\)

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