Question

figure h is the result of a transformation on figure g. which transformation would accomplish this? graph of figure g (a triangle in the first quadrant) and figure h (a triangle in the third quadrant) on a coordinate plane answer a translation 4 units to the left and 2 units down a rotation 180° counterclockwise about the origin a reflection over the x - axis a rotation 90° clockwise about the origin

Explanation:

To determine the transformation from Figure G to Figure H, we analyze each option:

• Translation 4 units left and 2 units down: The orientation of Figure H doesn't match a simple translation from G.
• Reflection over the x - axis: Reflecting over the x - axis would flip the figure vertically, but Figure H's orientation is not a vertical flip of G.
• Rotation 90° clockwise about the origin: A 90° clockwise rotation would change the figure's orientation in a way that doesn't match H.
• Rotation 180° counterclockwise about the origin: A 180° rotation about the origin maps a point \((x,y)\) to \((-x,-y)\). By examining the vertices of Figure G and Figure H, we can see that this rotation would align G to H. The relative positions and orientations of the triangles are consistent with a 180° counterclockwise rotation about the origin.

Answer:

A rotation \(180^\circ\) counterclockwise about the origin