Question

Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way to the same place from its original position. Hint: You may combine transformations.

Answer 1

Check picture 1

Notice that a 180° rotation clockwise or counterclockwise (around the origin) send any point P(a, b) to a point with coordinates (-a, -b).

this means the number values of the respective x and y coordinates are the same, but the signs are different.

for example rotating point P(-3, 17) 180 degrees results in point (3, -17)


check picture 2.

reflecting point P(a, b) with respect to :

the y-axis results in point (-a, b)


the x-axis results in point (a, -b)


for example , consider point P(-3, 17)

reflecting this point with respect to the y axis, results in (3, 17)

reflecting (3, 17) with respect to the x-axis results in (3, -17)


So the effect of reflecting with respect to the y axis, the x axis (the other way around is the same) results in the same point as rotating 180 degrees.


Answer:

1) reflect with respect to the y-axis, then reflect this last point with respect to the x-axis

2) reflect with respect to the x-axis, then reflect this last point with respect to the y-axis