Why Does Reflecting a Point Twice Across Parallel Lines Double the Distance?

In summary, the preimage that is reflected twice through two parallel lines located ten inches apart will be twenty inches away from the final image. This is because after each reflection, the point will be on the other side of the line, resulting in a total distance of 20 inches from the original point to the final image.
  • #1
terpsgirl
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a transformation question? HELP PLS

Hi, I have this question from classwork and I can't quite figure it out. I know its very simple, but I can't quite understand it...

If two parallel lines are located ten inches apart, a preimage that is reflected twice through those lines will be _________ inches away from the final image.

** I know the answer is twenty, but I'm not sure how/why.
Could someone help in explaining? It would be very appreciated!

Thanks
 
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  • #2
check out the attached file. i hope it will be clear from the picture. if not then feel free to tell me. you can also pm me or mail me at murshid_islam@yahoo.com.
 

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  • #3
terpsgirl said:
Hi, I have this question from classwork and I can't quite figure it out. I know its very simple, but I can't quite understand it...

If two parallel lines are located ten inches apart, a preimage that is reflected twice through those lines will be _________ inches away from the final image.

** I know the answer is twenty, but I'm not sure how/why.
Could someone help in explaining? It would be very appreciated!

Thanks

"Reflected twice through those lines"? I will assume that that means "reflected in each of the lines".

Imagine a point x inches from the first line (for simplicity, take x< 10 and the point is NOT between the two lines). After one reflection, the (image of the) point will be on the other side of the line (and so between the two lines) at distance x inches from it. What distance will it be from the second line now? Call that distance y. After the second reflection, the point will be on the other side of THAT line and the same distance from it. Okay, the total distance will be the original x inches plus the x inches on the other side, plus the y inches the first image was from the second line plus the y inches it was reflected to. What do all those add to?

Now see if you can do it assuming the original point is between the two lines or if it is more than 10 inches from the first line.
 

FAQ: Why Does Reflecting a Point Twice Across Parallel Lines Double the Distance?

1) What is a transformation question?

A transformation question is a type of question that asks for a change or conversion from one form or state to another. It can be used in various fields, such as mathematics, science, and psychology, to test a person's ability to think critically and creatively.

2) How do you approach solving a transformation question?

The first step in solving a transformation question is to carefully read and understand what is being asked. Then, break down the question into smaller parts and identify the given information and what needs to be transformed. Next, think about the possible methods or formulas that can be used to achieve the transformation. Lastly, check your answer and make sure it makes sense in the context of the question.

3) What skills does solving transformation questions develop?

Solving transformation questions helps to develop critical thinking, problem-solving, and analytical skills. It also encourages creativity and helps to improve logical reasoning and spatial awareness.

4) Are there any tips for solving transformation questions?

Some tips for solving transformation questions include practicing regularly, breaking down the question into smaller parts, using diagrams or visual aids to help with visualization, and checking your answer for accuracy and reasonableness. It is also helpful to understand the basic concepts and formulas related to the specific type of transformation question.

5) Can transformation questions be used for real-life applications?

Yes, transformation questions are often used in real-life applications, such as in engineering, computer graphics, and data analysis. They can also be used in decision-making processes, such as determining the most efficient route for travel or optimizing business processes.

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