Question

3 which sequence of transformations takes \\( \delta a \\) to its image, \\( \delta b \\)?
a reflection over the \\( x \\) - axis and translation 2 units down
b translation 2 units down and \\( 90 \\) rotation about the origin
c reflection over the \\( y \\) - axis and translation 2 units down
d translation 12 units right and \\( 90 \\) rotation about the origin

Explanation:

• First, check the reflection. Reflecting \(\triangle A\) over the \(y\) - axis changes the \(x\) - coordinates of its vertices. For example, if a vertex of \(\triangle A\) has coordinates \((x,y)\), after reflection over the \(y\) - axis, it becomes \((-x,y)\).
• Then, check the translation. Translating a figure \(2\) units down subtracts \(2\) from the \(y\) - coordinates of its vertices.

Answer:

C. reflection over the \(y\) - axis and translation \(2\) units down