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?

The reflection of the circle x2+y220x20y+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?

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?

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.

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 ab+cd?a - b + c - d?

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