Shape P is similar to shape Q, however, shape P, is smaller than shape Q.
- A single transformation that takes shape P to shape Q is; a dilation by a scale factor of 3 with a center of dilation at [tex]\underline{(1, \, 0)}[/tex].
Reasons:
The give figure shows;
The preimage figure = P
The image figure = Q
The image P is larger than the preimage Q, therefore, the figure, Q is a
dilation of the preimage P
The center of dilation is found with the formula;
[tex]x_0 = \mathbf{\dfrac{k \cdot x_1- x_2}{k - 1}}[/tex]
[tex]y_0 = \mathbf{\dfrac{k \cdot y_1- y_2}{k - 1}}[/tex]
Where;
(x₁, y₁) = A point on the preimage, P = (2, 3)
(x₂, y₂) = The corresponding point on the dilated image, Q = (4, 9)
k = The scale factor = 3
Therefore;
[tex]x_0 = \dfrac{3 \times 2-4}{3 - 1} = 1[/tex]
[tex]y_0 = \dfrac{3 \times 3- 9}{3 - 1} = 0[/tex]
The center of dilation, (x₀, y₀) = (1, 0)
Therefore;
The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0).
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