Geometry question

Question

Now consider stencil two. Again, use a combination of reflections, rotations, and translations to see whether stencil two will overlap with the original pattern. List the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement.

Answer 1

So, a reflection over the x-axis switches all the y values. (4,3) would move to (4,-3). Reflecting (4,3) over the y-axis moves it to (-4,3).

A rotation changes one or both the x and y values.

(4,3) rotated 90 degrees becomes (-3,4). Rotate it another 90 degrees (for 180 total) and you're at (-4,-3). Every rotation of 90 degrees results in (-y,x).

A translation just movesthe whole shape vertically or horizontally. Moving (4,3) down 5 puts it at (-1,3).

So, play with all of those to see if you can keep the same shape, rotate it, reflect it, and move it around to see if you can get it to match up with the original figure.

Let's take (4,3) and (2,3). I rotate my line 90 degrees and I have (-3,4) and (-3,2). I reflect that over the x-axis and I have (-4,-3) and (-2,-3). I reflect it now over the y-axis to (4,-3) and (2,-3). Move it down 2 to (4,-5) and (2,-5).

Have fun!