Question

figure v is the result of a transformation on figure u. which transformation would accomplish this?
answer
a translation 5 units down
a translation 5 units up
a reflection over the x - axis
a reflection over the y - axis

Explanation:

Step1: Analyze reflection over x - axis

A reflection over the x - axis changes the sign of the y - coordinate of each point. For a point \((x,y)\) on Figure U, after reflection over the x - axis, it becomes \((x, - y)\). By observing the coordinates of corresponding vertices of Figure U and Figure V, we can see that the y - coordinates of the vertices of Figure U are negated to get the y - coordinates of Figure V, while the x - coordinates remain the same.

Step2: Analyze other options

• A translation 2 units down would shift all points 2 units in the negative y - direction, but the relationship between Figure U and Figure V is not a simple vertical shift as the symmetry is about the x - axis.
• A translation 2 units up would shift all points 2 units in the positive y - direction, which does not match the transformation from Figure U to Figure V.
• A reflection over the y - axis would change the sign of the x - coordinate of each point, but the x - coordinates of Figure U and Figure V are the same, so this is not the case.

Answer:

A reflection over the x - axis