Question

(a) Draw the image of PQR after a rotation of 180° about the origin. Label the image P'Q'R' .

(b) Draw the image of PQR after a reflection across the x-axis. Label the image P"Q"R" .

Answer 1

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.