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.
Turn 1 Answer
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 $k$: $(-2 \times 2, 3 \times 2) = (-4,6)$
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:
$4 \times 3 = 12$
Response
Turn 1 Answer
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 $k$: $(-2 \times 2, 3 \times 2) = (-4,6)$
Answer
a. $(-4,6)$
Turn 2 Answer
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:
$4 \times 3 = 12$
Answer
d. The new rectangle has side lengths of 6 units and 12 units.