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1. Understand the question

   Turn 1 Question

   if a triangle is reflected over the y-axis and then dilated by a scale factor of 2, what will be the new coordinates of the point (2,3)?
   a. $(-4,6)$
   b. $(4,3)$
   c. $(-2,-6)$
   d. $(4,6)$

   Turn 2 Question

   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 9 units and 18 units. b. The new rectangle has side lengths of 3 units and 6 units. c. The new rectangle has side lengths of 4 units and 8 units. d. The new rectangle has side lengths of 6 units and 12 units.

2. Response

   Turn 1 Answer

3. Explanation

   Step1: Reflect over y-axis

   When reflecting a point $(x,y)$ over the y-axis, the x-coordinate flips sign: $(2,3) \to (-2,3)$

   Step2: Dilate by scale factor 2

   To dilate a point $(x,y)$ by scale factor $k$, multiply both coordinates by $k$: $(-2 \times 2, 3 \times 2) = (-4,6)$

4. Explanation

   Step1: Dilate first side length

   Multiply the 2-unit side by scale factor 3:
   $2 \times 3 = 6$

   Step2: Dilate second side length

   Multiply the 4-unit side by scale factor 3:
   $4 \times 3 = 12$

5. Final answer

   a. $(-4,6)$

   Turn 2 Answer

Answer

Question Analysis

OCR Text

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 9 units and 18 units. b. The new rectangle has side lengths of 3 units and 6 units. c. The new rectangle has side lengths of 4 units and 8 units. d. The new rectangle has side lengths of 6 units and 12 units.

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