Question

1. which figure is a reflection of figure a over the line x = -4? figure ____

Explanation:

Step1: Recall reflection rule

For a reflection over the vertical line $x = a$, the distance between each point of the original figure and the line $x = a$ is the same as the distance between its reflected - point and the line $x = a$. The $y$ - coordinate of each point remains the same during a reflection over a vertical line.

Step2: Analyze the position of figure A and line $x=-4$

The line $x = - 4$ is a vertical line. Figure A is to the left of the line $x=-4$. We need to find a figure that is at the same distance from the line $x = - 4$ on the right - hand side and has the same $y$ - coordinates for corresponding points.

Step3: Check each option

• Figure B is below figure A and not a reflection over $x=-4$.
• Figure C is too close to the $y$ - axis and not a reflection of figure A over $x = - 4$.
• Figure D has the correct position. The distance of figure A from the line $x=-4$ is the same as the distance of figure D from the line $x=-4$, and the $y$ - coordinates of corresponding points match.

Answer:

D