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QuestionMathematics

reflection across $x=- 1$
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Answer

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Step 1:
: Identify the given information and the task at hand.

We are given a line graph and are asked to find the coordinates of the reflected points about the line $x=-3$.

Step 2:
: Understand the reflection property.

Reflections have the following property: for any point $(a, b)$ on the graph, its reflection across the line $x=d$ is the point $(2d-a, b)$.

Step 3:
: Find the reflected points.

So, the reflected point C' is at $(-14, 1)$.
Let's find the reflected points for each point on the graph.

Step 4:
: Summarize the reflected points.

A' $(-10, 2)$, B' $(-12, 4)$, C' $(-14, 1)$.
The reflected points are:

Final Answer

The coordinates of the reflected points are A' $(- 10, 2)$, B' $(- 12, 4)$, C' $(- 14, 1)$.