Question

a. translation by 9 units left and 12 units down
b. dilation by scale factor of -2
c. translation by 2 units right
d. dilation by scale factor of 2

what is the result of applying a dilation with a scale factor of 3 to a rectangle with side lengths of 2 units and 4 units?
a. the new rectangle has side lengths of 3 units and 6 units.
b. the new rectangle has side lengths of 6 units and 12 units.
c. the new rectangle has side lengths of 4 units and 8 units.
d. the new rectangle has side lengths of 9 units and 18 units.

which transformation does not preserve the size of a figure?
a. dilation
b. rotation
c. reflection
d. translation

Explanation:

Step1: Solve first dilation question

Dilation scales all side lengths by the scale factor. For a scale factor of 3, multiply each original side length:
$2 \times 3 = 6$, $4 \times 3 = 12$

Step2: Solve second transformation question

Identify which transformation changes size: Dilation resizes figures, while rotation, reflection, translation only reposition/flip them without changing size.

Answer:

1. For the dilation rectangle question: b. The new rectangle has side lengths of 6 units and 12 units.
2. For the size-preserving transformation question: a. Dilation