Question

answer a reflection over the y -axis a translation 1 unit left and 4 units down a reflection over the x -axis a translation 4 units left and 1 unit down

Explanation:

Step1: Analyze transformation of key - points

Let's consider a point on Figure J, say the right - most vertex at (5,0). On Figure K, the corresponding vertex is at (1, - 4).

Step2: Calculate horizontal and vertical changes

The x - coordinate changes from 5 to 1, which means a change of \(5 - 1=4\) units to the left. The y - coordinate changes from 0 to - 4, which means a change of 4 units down.

Answer:

A translation 4 units left and 4 units down (Note: There is no such option exactly, but analyzing all options, the closest correct transformation conceptually is a translation. If we assume a mis - typing in options and consider the correct thought process, we analyze the changes in coordinates of vertices. Among the given options, the closest in nature is a translation. If we had to pick from the given options, we note the x - coordinate change and y - coordinate change. The x - coordinate of a point on Figure J to the corresponding point on Figure K moves left and y - coordinate moves down. A translation 4 units left and 1 unit down is the closest in terms of the x - coordinate movement among the given options). So the best option from the given ones is: A translation 4 units left and 1 unit down