Answer:
Reflection states that it is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.
(a)
The coordinates of triangle PQR from the given figure is:
P = (1, -1)
Q = (3 , -2)
R = (3 , -4)
To rotate a figure 180 degrees:
The rule of rotation of 180 degree :
\((x, y) \rightarrow (-x , -y)\)
Apply the above rule on PQR we have;
\(P(1, -1) \rightarrow P'(1 , -1)\)
\(Q(3, -2) \rightarrow Q'(2 , -3)\) and
\(R(3, -4) \rightarrow R'(4 , -3)\)
The label of image P'Q'R' as shown below in the figure:
(b)
The rule of reflection across the x-axis is:
\((x , y) \rightarrow (x , -y)\)
Apply the above rule on PQR triangle we get;
\(P(1, -1) \rightarrow P''(1 , 1)\)
\(Q(3, -2) \rightarrow Q''(3, 2)\)
\(R(3, -4) \rightarrow R''(3 , 4)\)
Label of image P"Q"R" as shown in the figure.
