Question

1. which transformation below would map the polygon a to the polygon b? image of coordinate plane with polygon a (green) and b (blue) options: polygon a has been translated to the right and reflected vertically. polygon a has been reflected horizontally and reflected vertically. polygon a has been rotated 180 degrees counterclockwise. polygon a has been translated down and then right.

Explanation:

1. Analyze each option:

• Option 1: Translating right and reflecting vertically. Let's check coordinates. Polygon A's vertices (approx: (-4,5), (-4,1), (-2,1)). Polygon B's vertices (1,-3), (1,1), (3,1). Translating A right (say 5 units: -4+5=1, -2+5=3) gives (1,5), (1,1), (3,1). Then reflecting vertically (over x - axis: (x,y)→(x, - y)) gives (1, - 5), (1, - 1), (3, - 1) which is not B. So incorrect.
• Option 2: Reflecting horizontally (over y - axis: (x,y)→(-x,y)) and then vertically (over x - axis: (x,y)→(x, - y)). For A's vertex (-4,5): reflect horizontally: (4,5), then vertically: (4, - 5) not matching B. Incorrect.
• Option 3: Rotating 180° counterclockwise: rule (x,y)→(-x, - y). For A's (-4,5): (4, - 5); (-4,1): (4, - 1); (-2,1): (2, - 1). Not matching B. Incorrect.
• Option 4: Translate down: A's y - coordinates decrease. From A's y≈5,1,1 to B's y≈-3,1,1: down by 4 (5 - 4 = 1? Wait, better to track a vertex. Take the top vertex of A: (-4,5). Move down to (-4,1) (down 4), then right to (1,1) (right 5). Another vertex: (-4,1)→(-4,1) down? No, wait B's bottom vertex is (1, - 3). Wait, maybe better: A's vertices: let's list properly. A: let's say points are (-4,5), (-4,1), (-2,1). B: (1,-3), (1,1), (3,1). Translate A down: from y = 5 to y=-3: down 8? No, maybe step by step. Translate down: take (-4,5)→(-4,1) (down 4), then right to (1,1) (right 5). (-4,1)→(-4,1) down? No, (-4,1)→(1,1) (right 5), then down to (1,-3) (down 4). (-2,1)→(3,1) (right 5), then down? No, (3,1) is a vertex of B. So translating down (vertical movement) and then right (horizontal movement) matches the positions. So this option is correct.

Answer:

Polygon A has been translated down and then right.