Question

1. identify the sequence of transformations that will reflect a figure over the x-axis and then dilate it by a scale factor of 3 to create a similar figure.

a. $(x,y) \to (x,-y); (x,y) \to (3x,3y)$
b. $(x,y) \to (-x,y); (x,y) \to (x,3y)$
c. $(x,y) \to (x,-y); (x,y) \to (3x,y)$
d. $(x,y) \to (-x,y); (x,y) \to (3x,3y)$

Explanation:

Step1: Recall x-axis reflection rule

A reflection over the x-axis transforms a point $(x,y)$ to $(x,-y)$, since the y-coordinate is negated.

Step2: Recall dilation by scale factor 3

A dilation with scale factor 3 (centered at the origin) multiplies both coordinates by 3, transforming $(x,y)$ to $(3x,3y)$.

Step3: Match to options

Combine the two transformations in order: first $(x,y)\to(x,-y)$, then $(x,y)\to(3x,3y)$.

Answer:

a. $(x, y) \to (x, -y); (x, y) \to (3x, 3y)$