Coordinates of the given triangle:
P (1,-1)
Q (3,-2)
R (3,-4)
A) we need to apply transformation "180 degree about the origin".
If we have (x,y) coordinates of the given triangle.
On rotating 180 degrees about origin, we get (-x,-y) coordinates of the transformed triangle.
Therefore, we can apply rule (x,y) --> (-x,-y) for a part.
By applying above rule, we get new coordinates of the transformed triangle:
P (1,-1) ---> P'(-1,1)
Q (3,-2) ---> Q'(-3,2)
R (3,-4) ---> R'(-3,4)
Now, we can plot those coordinates on the graph.
B) we need to reflect Triangle P'Q'R' across x-axis.
If we have (h,k) coordinates of the P'Q'R' triangle.
On reflecting Triangle P'Q'R' across x-axis, only y coordinates would get multiply by -1 and we get (h,-k) coordinates of the reflected triangle.
Therefore, we can apply rule (h,k) --> (h,-y) for b part.
By applying above rule, we get new coordinates of the transformed triangle:
P'(-1,1) ---> P"(-1,-1)
Q'(-3,2) ---> Q"(-3,-2)
R'(-3,4) ---> R"(-3,-4)
Now, we can plot those coordinates on the graph.
