4.1 Warm-Up Tuesday
Video Example:

Write the algebraic rule that represents the dilation that was applied.

You Try:

Which rule best represents the dilation that has been applied?

(x, y) → (2x, y)

(x, y) → (0.5x, 0.5y)

(x, y) → (2x, 2y)

(x, y) → (2 + x,2 + y)

Wednesday
Video Example:
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’. Which statement is true?

Triangle A’B’C’ is larger than Triangle ABC, because the scale factor is greater than 1

Triangle A’B’C’ is smaller than Triangle ABC, because the scale factor is less than 1

Triangle A’B’C’ is smaller than Triangle ABC, because the scale factor is greater than 1

You Try:
A figure will be dilated on a coordinate grid to create a smaller figure. The figure is dilated using the origin as the center of dilation. Which rule could represent this dilation?

(x, y) (0.5 + x, 0.5+y)

(x, y) (0.5 - x, 0.5-y)

(x, y) (32x, 32y)

(x, y) (23x, 23y)

The answer is below

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.

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x