Question

a reflection over the y-axis followed by a translation down 6 units. try
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Analyze Reflection Over y - axis

When a point \((x,y)\) is reflected over the \(y\) - axis, the transformation rule is \((x,y)\to(-x,y)\). Let's consider a vertex of the original figure, say point \(A\). Suppose the original coordinates of \(A\) are \((2, - 2)\) (from the graph). After reflection over the \(y\) - axis, it becomes \((-2,-2)\).

Step2: Analyze Translation Down

A translation down by \(n\) units means subtracting \(n\) from the \(y\) - coordinate of the point. Let's check the vertical distance between the reflected figure and the final figure. Looking at the \(y\) - coordinates of corresponding points (e.g., the bottom - most points of the figures), we can see that the translation down is 6 units. For example, if a point after reflection has a \(y\) - coordinate of \(-2\), after translating down 6 units, the new \(y\) - coordinate is \(-2-6=-8\), which matches the coordinates of the corresponding point in the final figure.

Answer:

The translation down is 6 units. So the number in the box should be 6.