Question

question
figure n is the result of a transformation on figure m. which transformation would accomplish this?
answer
a translation 2 units up
a translation 2 units down
a reflection over the x - axis
a reflection over the y - axis

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation or reflection. If it were a translation 2 units up, all points of Figure M would move 2 units vertically up. If it were a translation 2 units down, all points of Figure M would move 2 units vertically down. But the orientation of Figure N compared to Figure M (if we assume a general position - looking at the y - coordinate change of corresponding vertices) is not just a simple up - down shift. For example, if we consider a vertex of Figure M at \((x,y)\) and a corresponding vertex of Figure N at \((x,y + 2)\) (for up) or \((x,y-2)\) (for down). But we can also check the symmetry.

Step2: Analyze reflection

Reflection over the \(x\) - axis changes the sign of the \(y\) - coordinate of each point. If we have a point \((x,y)\) in Figure M, after reflection over the \(x\) - axis, it becomes \((x, - y)\). If we assume a vertex of Figure M is \((x,y)\) and a corresponding vertex of Figure N is \((x, - y)\) (by observing the vertical position relative to the \(x\) - axis). For example, if Figure M has a point close to \(y=-2\) and Figure N has a corresponding point close to \(y = 2\) (a change in the sign of the \(y\) - coordinate). Reflection over the \(y\) - axis changes the sign of the \(x\) - coordinate (\((x,y)\to(-x,y)\)). But looking at the position of the figures relative to the \(x\) - axis (the horizontal axis), we can see that Figure N is the mirror - image of Figure M across the \(x\) - axis.

Answer:

A reflection over the \(x\) - axis