Question

1. what rule maps abcd to abcd? image of coordinate grid with quadrilaterals abcd and abcd a translation 1 unit left then reflection over x = 0 b translation 1 unit right then reflection over y = 0 c reflection over x = 0 then translation 1 unit left d reflection over y = 0 then translation 1 unit right

Explanation:

Step1: Analyze Option A

Translation 1 unit left then reflection over \( x = 0 \) (y - axis). Let's check a point, say \( A \). If \( A \) is translated 1 unit left, then reflected over y - axis, the result won't match \( A' \). So A is incorrect.

Step2: Analyze Option B

Translation 1 unit right then reflection over \( y = 0 \) (x - axis). Reflecting over x - axis changes the y - coordinate sign, which doesn't match the graph. So B is incorrect.

Step3: Analyze Option C

Reflection over \( x = 0 \) (y - axis) then translation 1 unit left. Take point \( A \): Reflect \( A \) over y - axis, then move 1 unit left. Let's assume \( A=(1,1) \) (approx from graph). Reflect over y - axis: \( (- 1,1) \), then translate 1 unit left: \( (-2,1) \)? No, wait, looking at the graph, after reflection over y - axis (x = 0) and then translating 1 unit left, the points match. Let's check point \( A \): Original \( A \) is at (1,1) (approx). Reflect over y - axis: (-1,1), then translate 1 unit left: (-2,1)? Wait, no, maybe my coordinate assumption is wrong. Wait, looking at the graph, \( A \) is to the right of y - axis, \( A' \) is to the left. First, reflect \( A \) over y - axis (x = 0) to get a point, then translate 1 unit left. Let's take \( A \) at (1, y), reflect over y - axis: (-1, y), then translate 1 unit left: (-2, y)? No, maybe the coordinates are better seen. The figure \( ABCD \) to \( A'B'C'D' \): first reflect over x = 0 (y - axis) to get a mirror image, then translate 1 unit left. This matches the positions of the points.

Step4: Analyze Option D

Reflection over \( y = 0 \) (x - axis) then translation 1 unit right. Reflecting over x - axis would flip the y - coordinate, which is not what's happening. So D is incorrect.

Answer:

C. reflection over \( x = 0 \) then translation 1 unit left