Question

figure a is the result of a transformation on figure j. which transformation would accomplish this? answer a reflection over the y -axis a reflection over the x -axis a translation 1 unit left and 4 units a translation 4 units left and 1 unit

Explanation:

Step1: Analyze reflection over y - axis

For a reflection over the y - axis, the rule is $(x,y)\to(-x,y)$. Points of Figure J would change their x - coordinates' sign. But Figure K is not a y - axis reflection of Figure J.

Step2: Analyze reflection over x - axis

For a reflection over the x - axis, the rule is $(x,y)\to(x, - y)$. If we take points of Figure J and apply this rule, we get the points of Figure K. For example, a point $(x,y)$ on Figure J becomes $(x,-y)$ on Figure K.

Step3: Analyze translations

A translation 1 unit left and 4 units down has the rule $(x,y)\to(x - 1,y - 4)$. A translation 4 units left and 1 unit down has the rule $(x,y)\to(x - 4,y - 1)$. These do not map Figure J to Figure K.

Answer:

A reflection over the x - axis