Question

Describe fully the single transformation that takes place from shape P to Q

Answer 1

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).

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 .

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;

`x_(0) = (k*x_(1) - x_(2))/(k - 1)\\y_(0) = (k*y_(1) - y_(2))/(k - 1)`

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;

`x_(0) = (3 * 2 - 4)/(3 - 1) = 1\\y_(0) = (3 * 3 - 9)/(3 - 1) = 0`

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).