+4625 Triangle ABC with vertices of A(6,2) , B(2,5) , and C(2,2) is reflected over the x-axis to triangle A′B′C′ . This triangle is reflected over the y-axis to triangle A″B″C″ . What are the coordinates of point C ?
+2446 Yes, Point C is at (-2,-2) when reflected over the x-axis and then over the y-axis.
+2446 You don't have to graph this to figure out the answer. Just know the relationships (although I prefer graphing than remembering the relationships.
A reflection over the x-axis has the following effect:
(x,y)−−−>(x,−y)
A reflection over the y-axis has the following effect:
(x,y)−−−>(−x,y)
Let's try this with point C at (2,2):
First, you reflect over the x-axis. This arrow notation says that the x-coordinate does not change but the y-coordinate changes to -1*y-coordinate:
(2,2)−−−>(2,−2),so C′(2,−2)
Take C' and apply the effect of reflecting over the y-axis:
(2,−2)−−−>(−2,−2),so C″(−2,−2)
Hopefully, this makes sense. This is simply another method of solving. If you want to stick to graphing, that is OK.
