What is the line of reflection in geometry?

The line of reflection is the line at which all points of a shape are moved across . Each point and its corresponding point are the same distance across the line of reflection. To determine the line of reflection imagine folding the graph so that each point on the original figure matches its point on the image.

How to reflect a shape in geometry?

To reflect an object, you need a mirror line . When a shape is reflected, its size does not change - the image just appears 'flipped'. Every point on the shape is the same distance away on the other side of the mirror line. Using squared paper can be very handy to help you reflect an object.

When a point or shape is flipped across a line, creating a mirror image.?

A reflection is a transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite sides of the line of reflection. The line of reflection can be defined by an equation or by two points it passes through.

What is the formula for reflection?

Here is the general rule for reflection across the y-axis: Given an equation y = f ( x ) , the new reflection equation of the reflected graph will be y = f ( − x ) .

What does y^2 mean in reflections?

If we reflect about the line y = 2, then the original point and its image have the same x-coordinate and have y-coordinates that average to 2 (and so add to twice 2, or 4). So the image of any point (x, y) would be (x, 4-y). For example, the image of (6, 5) would be (6, 4-5) = (6, -1).

What is the rule for reflection?

Reflection Rules Reflection Reflection Rule In Words Over the x-axis (x,y)-->(x,-y) Negate the y coordinates Over the y-axis (x,y)-->(-x,y) Negate the x coordinates Over y=x (x,y)-->(y,x) Swap the x and y coordinates Origin (x,y)-->(-x,-y) Negate both the x and y coordinates

What is the formula for the reflection of a point about the line?

When a point is reflected across the line y = x, the x-coordinates and y-coordinates change their place. Similarly, when a point is reflected across the line y = -x, the x-coordinates and y-coordinates change their place and are negated. Therefore, The reflection of the point (x, y) across the line y = x is (y, x) .

What is a transformation of a figure that flips the figure across a line?

A reflection is a flip over a line.

How can you reflect a polygon on a graph?

Reflecting a Polygon Across the -Axis Step 1: Identify and label each vertex of the polygon with its coordinates . Step 2: Find the reflection across the -axis of each vertex from step 1 by replacing the -coordinate with its opposite, . Plot these reflected vertices on the graph.

What is another name for the line of reflection?

The line of reflection is also called the mirror line .

Which represents the line of reflection?

The line that the shape is reflected across is called the line of reflection, and each of the points on the original shape will be the same distance from the line of reflection as their corresponding points on the reflected shape are from the line of reflection.

Reflections review (article) | Reflections

Review the basics of reflections, and then perform some reflections.

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Ultimate Hope
6 years agoPosted 6 years ago. Direct link to Ultimate Hope's post “Hw do I make the line go ...”
Hw do I make the line go where I want it, I'M SO CONFUSED!?
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(39 votes)
- StellaAndShardBear
  4 years agoPosted 4 years ago. Direct link to StellaAndShardBear's post “To move the line where yo...”
  To move the line where you want it to be, click/tap and hold down the dot to move it. Hope this helps!
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  (7 votes)
Valerie
7 years agoPosted 7 years ago. Direct link to Valerie's post “a little bit troubling so...”
a little bit troubling some tips plz
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(33 votes)
- A B
  6 years agoPosted 6 years ago. Direct link to A B's post “How to do the practice: ...”
  How to do the practice:
  For the question: "Use the "Reflect" tool to find the image of MN for a reflection over the line y=-x+1".
  First hit the "Reflect" button.
  See Also
  Reflecting shapes (article) | Reflections | Khan Academy Reflections in math. Formula, Examples, Practice and Interactive Applet on common types of reflections like x-axis, y-axis and lines:8.14: Rules for Reflections Triangle Reflection - Definition, Techniques, and Examples - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day
  Then move the line to the center of the grid by moving your mouse over the line, away from the arrows, until the cursor changes to the icon you recognize as allowing for moving. Move the line to the center of the grid. Then decide the slope the line needs to have. Here it is -1, so use the rotation arrows to change the slope to -1. Then determine the y-intercept. Here that is 1. So, move the line so that it goes through the y-intercept (0,1). Finally, hit one of the arrows on either side of the line to reflect the image.
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  (5 votes)
Elena Kolesneva
6 years agoPosted 6 years ago. Direct link to Elena Kolesneva's post “i dont understand the lin...”
i dont understand the line of reflection in a form of an equation. there's smth missing here. is there a video?
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(15 votes)
- JAYDEN JONES
  2 years agoPosted 2 years ago. Direct link to JAYDEN JONES's post “understand that the same ...”
  understand that the same distance away from the x-axis and the y-axis. there you will find your answer. keep practicing.
  Comment on JAYDEN JONES's post “understand that the same ...”
  (1 vote)
Darren Drake
5 years agoPosted 5 years ago. Direct link to Darren Drake's post “Hi There.In the "Perfor...”
Hi There.
In the "Performing Reflections" I see the conventional equation is y=mx +b
Then the first example below it gives: y=x
which means that "the y intercept is 0 and the slope is 1".
Is there a video explaining how the slope is determined for the line of reflection? It feels like a formula, or equation, with rules that make no sense to me. <grin>
I can reflect shapes, and rotate shapes, across a line of reflection - no problem. I cannot see how the line of reflection is originally determined from the formula. Particularly, the slope.
What am I missing? I might have jumped a step somewhere, I don't know.
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(9 votes)
- kubleeka
  5 years agoPosted 5 years ago. Direct link to kubleeka's post “Take a point A, and refle...”
  Take a point A, and reflect it across a line so that it lands at B. Join segment AB. The reflecting line will be a perpendicular bisector of AB.
  So if you know the coordinates of A and B, you can determine the slope of AB. Because they're perpendicular, you can then determine the slope of the reflecting line.
  Also, since you know the coordinates of A and B, you can find their midpoint, which will be on the reflecting line. So now you have the slope of the reflecting line and a point on it, and can find an equation for it.
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  (7 votes)
  See Also
  Determining reflections (video) | Khan Academy
allecoth3546
2 years agoPosted 2 years ago. Direct link to allecoth3546's post “how did everyone find thi...”
how did everyone find this so hard! It's so easy.
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(9 votes)
cooperbadeer
4 years agoPosted 4 years ago. Direct link to cooperbadeer's post “im never gonna need to kn...”
im never gonna need to know this
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- David Severin
  4 years agoPosted 4 years ago. Direct link to David Severin's post “You will need it to pass ...”
  You will need it to pass high school and maybe college. Artists, Architects, Designers (including video game designers), and others need to know it also.
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  (14 votes)
Alvin Izera
4 years agoPosted 4 years ago. Direct link to Alvin Izera's post “what if a value of y is g...”
what if a value of y is given like....reflect across y=2
then ?? how to solve this?
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- Ian Pulizzotto
  4 years agoPosted 4 years ago. Direct link to Ian Pulizzotto's post “Good question!If we ref...”
  Good question!
  If we reflect about the line y = 2, then the original point and its image have the same x-coordinate and have y-coordinates that average to 2 (and so add to twice 2, or 4).
  So the image of any point (x, y) would be (x, 4-y). For example, the image of (6, 5) would be (6, 4-5) = (6, -1).
  More generally, the image of any point (x, y) under reflection about the line y=b would be (x, 2b-y). Similarly, the image of any point (x, y) under reflection about the line x=a would be (2a-x, y). The concept of averaging in one coordinate and equality in the other coordinate leads to these formulas.
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  (5 votes)
harundiyarip
4 years agoPosted 4 years ago. Direct link to harundiyarip's post “your videos makes me smar...”
your videos makes me smarter, THANK YOU i appreciate it
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(6 votes)
christopher.shinn
7 years agoPosted 7 years ago. Direct link to christopher.shinn's post “i had some trouble with t...”
i had some trouble with these
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28040
10 months agoPosted 10 months ago. Direct link to 28040's post “what job is this for?”
what job is this for?
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- 660832
  2 months agoPosted 2 months ago. Direct link to 660832's post “what does it mean if you...”
  what does it mean if you did the problem correct but it says it is wrong ?
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Reflections review (article) | Reflections | Khan Academy (2024)

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FAQs

What is the line of reflection in geometry? ›

Which represents the line of reflection? ›

Reflection	Reflection Rule	In Words
Over the x-axis	(x,y)-->(x,-y)	Negate the y coordinates
Over the y-axis	(x,y)-->(-x,y)	Negate the x coordinates
Over y=x	(x,y)-->(y,x)	Swap the x and y coordinates
Origin	(x,y)-->(-x,-y)	Negate both the x and y coordinates