Triangle LMN is reflected across a line, L = (12, –7), and L’ = (–7, 12). What is the line of reflection?
the x-axis
the y-axis
the line y = x
the line y = –x

Option C: The line is the line of reflection.

Explanation:

It is given that the across a line, and

Thus, the reflection is given by ⇒

Now, we shall determine the line of reflection.

Option A: the x-axis

To reflect the coordinates across x-axis is given by ⇒

Thus, the line of reflection of the coordinate L across x-axis is given by  

⇒

This is not the equal to the given line of reflection ⇒

Hence, the line of reflection is not across x-axis.

Thus, Option A is not the correct answer.

Option B : the y-axis

To reflect the coordinates across x-axis is given by ⇒

Thus, the line of reflection of the coordinate L across y-axis is given by  

⇒

This is not the equal to the given line of reflection ⇒

Hence, the given line of reflection is not across y-axis.

Thus, Option B is not the correct answer.

Option C: the line

To reflect the coordinates across is given by ⇒

Thus, the line of reflection of the coordinate L across the line is given by ⇒

This is equal to the given line of reflection ⇒

Hence, the given line of reflection is across the line

Thus, Option C is the correct answer.

Option D : the line

To reflect the coordinates across is given by ⇒

Thus, the line of reflection of the coordinate L across the line is given by ⇒

This is not the equal to the given line of reflection ⇒

Hence, the given line of reflection is not across the line .

Thus, Option D is not the correct answer.

answer: c is correct, a regular pentagon

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