# [ASK] Reflection of a Line by Another Line

• MHB
• Monoxdifly
In summary, a reflection of a line by another line is a geometric transformation that involves flipping a line over another line, resulting in a mirrored image of the original line. This is different from a rotation or translation, which involve different types of movements. The mathematical equation for a reflection of a line by another line depends on the orientation of the reflecting line. A reflection of a line by another line can result in the same line if certain conditions are met. In real life, reflections of lines are used in various applications such as creating symmetrical designs, constructing mirrored structures, and in optics for creating mirrored images.
Monoxdifly
MHB
The reflection of the line 5x - 7y - 13 = 0 by the line y = -x is ...
A. 7x + 5y - 13 = 0
B. 7x + 5y + 13 = 0
C. 7x - 5y - 13 = 0
D. 7x - 5y + 13 = 0
E. 7y + 5x + 13 = 0

This one I totally have no idea. Like, at all.

If we let:

$$\displaystyle y=-x$$

and

$$\displaystyle x=-y$$

in the given line, what do we obtain?

-5y + 7x - 13 = 0?

Monoxdifly said:
-5y + 7x - 13 = 0?

Correct. :)

I can't believe that out of the 4 questions I asked tonight, the one I found the hardest was the one with the simplest step.

## 1. What is a reflection of a line by another line?

A reflection of a line by another line is a geometric transformation that involves flipping a line over another line. This results in the original line being mirrored across the reflecting line.

## 2. How is a reflection of a line by another line different from a rotation or translation?

A reflection involves flipping the original line over another line, while a rotation involves rotating the line around a fixed point, and a translation involves moving the line without changing its orientation.

## 3. What is the mathematical equation for a reflection of a line by another line?

The equation for a reflection of a line by another line is (x,y) -> (-x,y) for a horizontal reflecting line and (x,y) -> (x,-y) for a vertical reflecting line.

## 4. Can a reflection of a line by another line result in the same line?

Yes, a reflection of a line by another line can result in the same line if the reflecting line is the line itself or if the line is perpendicular to the reflecting line.

## 5. How is a reflection of a line by another line used in real life?

A reflection of a line by another line is used in real life to create symmetrical designs and patterns. It is also used in architecture and construction to create mirrored structures and in optics to create mirrored images.

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