Question

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

Answer 1

A - when doing a 180 degree rotation, the coordinates (x,y) would become (-x,-y), in other words, the inverse of the numbers in the x and y places, (-1,2)->(1,-2)
B - when reflecting over the x axis, only the y coordinate inverts, (x,y) becomes (x,-y), (1,-2)->(1,2)

Answer 2

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.