Question

1. figure a and its image after a transformation, figure a, are shown on the coordinate plane below. which transformation of figure a demonstrates the congruence between the two figures? a a translation 8 units down b a reflection over the x - axis c a reflection over the y - axis d a rotation of 180° about the origin

Explanation:

To determine the transformation, we analyze each option:

• Option A: A translation 8 units down would move the figure vertically, but the figures are symmetric about the y - axis, not a vertical translation.
• Option B: A reflection over the x - axis would flip the figure over the x - axis, but the orientation and position relative to the y - axis suggest otherwise.
• Option C: A reflection over the y - axis: If we take a point \((x,y)\) on Figure A, its image after reflection over the y - axis is \((-x,y)\). By observing the coordinates of corresponding points on Figure A and Figure A', we can see that this reflection maps Figure A to Figure A' and preserves congruence (since reflection is a rigid transformation).
• Option D: A rotation of \(180^{\circ}\) about the origin would map \((x,y)\) to \((-x,-y)\), which does not match the relationship between the two figures.

Answer:

C. a reflection over the y - axis