Question

(a) Using Geometry Vocabulary, describe a sequence of transformations that maps figure P onto figure Q.

(b) Write the Transformation Mapping Rule(s) for the sequence you described in part (a).

Question 1 options:

Answer 1

A composite transformation is the transformation of a figure by two or more transformations

The correct descriptions and rules are:

(a) The transformation description;  The sequence of transformation that maps figure P onto figure Q is a 90 degrees clockwise rotation, followed by a translation of 6 units downwards (-6 units) maps figure P onto Q

(b) The Transformation Mapping Rules are; $\underline {R_{O, -90} }$ and $\underline {T_{0, -6}}$

The given parameters;

The coordinates of the vertices of the preimage, figure P, are;

(-1, 2), (-1, 4), (-4, 2), and (-4, 4)

The coordinates of the vertices of the image, figure Q, are;

(2, -2), (4, -2), (4, -5), and (2, -5)  

(a) The description of the sequence of transformations that maps figure P onto figure Q are;

A 90 degrees clockwise rotation about the origin, to transform (x, y) to (y, -x), which gives;

90° clockwise rotation = $R_{-90}$

(-1, 2) $\underset \longrightarrow {R_{O, -90} }$ (2, 1)

(-1, 4) $\underset \longrightarrow {R_{O, -90} }$  (4, 1)

(-4, 2) $\underset \longrightarrow {R_{O, -90} }$  (2, 4)

(-4, 4) $\underset \longrightarrow {R_{O, -90} }$  (4, 4)

The x-coordinates values of the image due to the rotation are equal to the x-coordinate values of the coordinates of the vertices of figure Q, while the difference in the y-values are -5 - 1 = -6

Therefore, the image obtain trough the rotation of figure P is translated vertically by -6 units (downwards), $T_{0, -6}$, to completely map figure P onto figure Q

Therefore, the description of the sequence of transformation that maps figure P onto figure Q is a 90 degrees clockwise rotation, followed by a translation of 6 units downwards (-6 units) maps figure P onto Q

(b) The Transformation Mapping Rule for the sequence described in part (a) are;

$\mathbf{{R_{O, -90} }}$ = 90 degrees clockwise rotation about the origin of points on figure P, followed by

$\mathbf{T_{0, -6}}$ = A translation of 6 units downwards

The composite transformation is $T_{0, -6}\circ {R_{O, -90} }$

Learn more about composite transformations here:

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