[Pic] Describe a combination of transformations.

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SchulzD · Accepted Answer

From the figure, rectangle DEFG has vertices of D(6,3), E(5,3), F(5,−3), and G(6,−3) and rectangle D''E''F''G' has vertices of D''(−12,6),E''(−10,6), F''(−10,−6),and G''(−12,−6). Since rectangle DEFGDEFG is on the right side of the yy-axis and rectangle D''E''F''G''′ is on the left side of the yy-axis, the first transformation is a reflection across the yy-axis. To reflect a point across the y-axis, use the rule (x,y) $\to$ (−x,y):
(x,y) $\to$ (−x,y)
D(6,3) $\to$ D′(−6,3)
E(5,3) $\to$ E′(−5,3)
F(5,−3) $\to$ F′(−5,−3)
G(6,−3) $\to$ F′(−6,−3)
Notice that the coordinates of the vertices of rectangle D''E''F''G''′ are twice the coordinates of the vertices of rectangle D′E′F′G. The second transformation is then a dilation by a scale factor of 2 centered at the origin. To dilate a point by a scale factor of k centered at the origin, use the rule $(x, y) \to (k x, k y) :$
$(x, y) \to (2 x, 2 y)$
$D' (- 6, 3) \to D'' (- 6 \cdot 2, 3 \cdot 2) = D'' (- 12, 6)$
$E' (- 5, 3) \to E'' (- 5 \cdot 2, 3 \cdot 2) = E'' (- 10, 6)$
$F' (- 5, - 3) \to F'' (- 5 \cdot 2, - 3 \cdot 2) = F'' (- 10, - 6)$
$G' (- 6, - 3) \to G'' (- 6 \cdot 2, - 3 \cdot 2) = G'' (- 12, - 6)$ The combination of transformations used to obtain rectangle D''E''F''G''′ was then a: reflection across the y−axis and a dilation by a scale factor of 2 centered at the origin

[Pic] Describe a combination of transformations.

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