Question

4.1 Warm-Up

Answer 1

Answer:

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Step-by-step explanation:

The question is not complete but i would show how to solve.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are dilation, rotation, translation and reflection.

Dilation is the enlargement or reduction in the size of a figure.

a) If an point A(x, y) is dilated by a factor k, the new coordinate is A'(kx, ky). From the above options the ones that represent dilation is (x, y) → (0.5x, 0.5y)  and (x, y) → (2x, 2y) . If the object is reduced then the correct option is (x, y) → (0.5x, 0.5y)   while if the object is enlarged the correct option is (x, y) → (0.5x, 0.5y)

b)Dilation is the enlargement or reduction in the size of a figure by a factor k. If k < 1, then it is a reduction and if k > 1, it is an enlargement.

Since Triangle XYZ is dilated with the origin as the center of dilation using the rule (x, y)⇒(0.5x, 0.5y) to create Triangle X’Y’Z’, since the factor is less than 1(0.5 < 1), it is a reduction. Hence Triangle X’Y’Z’ is smaller than Triangle XYZ, because the scale factor is less than 1

c) The dilation creates a smaller figure hence the factor of dilation should be less than 1.