Question

figure h is the result of a transformation on figure g. which transformation would accomplish this?
answer
a rotation 180° counterclockwise about the origin
a reflection over the y -axis
a reflection over the x -axis
a translation 2 units down

Explanation:

Step1: Analyze Reflection over x - axis

A reflection over the x - axis changes the sign of the y - coordinate of a point \((x,y)\) to \((x, - y)\). Let's take a vertex of Figure G, say if a vertex of G is \((x,y)\), after reflection over x - axis, it becomes \((x, - y)\). Looking at the figures, Figure H is above the x - axis and Figure G is below the x - axis. For example, if we take a corresponding vertex of G and H, the y - coordinates are negatives of each other (up to the position).

Step2: Analyze other options

• Rotation \(180^{\circ}\) counterclockwise about the origin: This would change \((x,y)\) to \((-x, - y)\), which is not the case here as the x - coordinates of corresponding vertices seem to be the same (or follow reflection over x - axis pattern).
• Reflection over y - axis: Changes \((x,y)\) to \((-x,y)\), which does not match the position of H relative to G.
• Translation 2 units down: This would move G further down, not up to H's position.

Answer:

A reflection over the x - axis