reflection and translation

Question

Draw a figure on a coordinate grid. a) Choose a translation and/or a reflection that you could repeatedly apply to the figure and its images to make a design or pattern. b) Does the figure tessellate? If your answer is no, could you change the transformation to make it tessellate? Explain.

please draw this , i am very confused

thanxx

Answer 1

The geometrical figure above with its reflections is an example. The figure in red is the original figure and the reflection of the figure in both axes is shown in black. The axes act like mirrors in a kaleidoscope to produce a symmetrical figure. Tesselation is possible in this case if the "tile" enclosing the figure (rectangle measuring 4 by 2 units) is repeated along each axis so that the pointed parts touch, as illustrated below (axes removed, but original figure shown in red):

Comments

its awesome but can u make some thing easy 

i made something ,can u pls chk it out

thanx

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I assume the blue lines are the axes. You reflected the figure in the first quadrant in the y-axis and produced what is in the 2nd quadrant. You can reflect the first quadrant into the 4th quadrant and the 2nd quadrant into the 3rd quadrant. The rectangle 12 x 16 produced by the reflections in all quadrants produces your tile, which propagates over the whole grid indefinitely to give you the tesselation. The tile would then have total symmetry to form your design.

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ok thank u so much sir , i am going to make the figure using your instruction then will submit here :)

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now is it correct ? please check 

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You seem to have introduced an extra 4x2 rectangle in the reflection in quadrants 3 and 4. Assuming the blues lines are axes, we have a design that reaches up to y=3 but below the x-axis the design reaches y=-5.  There is also a solid red line from (-6,-3) to (6,-3) below the x-axis at y=-3, but the line is not continuous between (-2,3) and (2,3) above the axis. To check reflections, simply invert the picture. It should look exactly the same. The enclosing rectangle is 12x6.