A composition transformation consists of the combination of two or more transformations
The correct option for the rule that describes the composition transformations that maps figure PQRS to P''Q''R''S'' is [tex]\underline{r_l \bullet R_{Q, \ 180^{\circ}}}[/tex]
The procedure by which the above option was selected is given as follows:
The coordinates of the image of a point (x, y) following a rotation of 180° about the origin is (-x, -y)
Taking point Q as the origin of rotation, (0, 0), we have;
Image of (0, 0), following a rotation is (-0, -0) = (0, 0)
- Point S is the lowest and the rightmost point below point Q, and therefore, the image of Q(x, y) = Q'(-x, -y) will be the highest and leftmost point after the rotation.
- Similarly for points P → P', and R → R'
Therefore;
Figure P'Q'R'S' is obtained from PQRS by a rotation of 180° about the point Q, by [tex]R_{Q, \ 180^{\circ}}[/tex]
Transformation from figure P'Q'R'S' to P''Q''R''S'':
The x-coordinates of figures P'Q'R'S' and PQRS are the same, while the corresponding points have the same vertical distance from the line l, such that the transformation of P'Q'R'S' to PQRS is given as follows, taking the line l as the x-axis;
(x, y) transformation (x, -y), which is equivalent to a reflection across the x-axis or line l, therefore, we have;
Transformation from figure P'Q'R'S' to P''Q''R''S'' is [tex]r_l[/tex]
The composition of transformations that maps PQRS to P''Q''R''S'' is therefore;
[tex]r_l \bullet R_{Q, \ 180^{\circ}}[/tex]
Learn more about composition transformation here;
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