Geometry

Isometries

Reflection

         

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

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The reflection of the circle x2+y2−20x−20y+196=0x^2+y^2-20x-20y+196=0 in the origin (0,0) (0,0)\ is  x2+y2+ax+by+c=0.\ x^2+y^2+ax+by+c=0. What is a+b+ca+b+c?

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

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If rectangle ABCDABCD in the above graph is reflected in the line y=−1,y = -1, what is the image of point D?D? The side length of each square in the graph paper is 1.1.

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

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