Determining reflections (video) | Khan Academy (2024)

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  • ramona.spencer

    5 years agoPosted 5 years ago. Direct link to ramona.spencer's post “are there any tricks or r...”

    are there any tricks or rules with rigid transformations?

    (20 votes)

    • njeevan

      5 years agoPosted 5 years ago. Direct link to njeevan's post “I can't think of any tric...”

      Determining reflections (video) | Khan Academy (4)

      I can't think of any tricks, but I do know a rule:
      A rigid transformation only occours if the 2nd image of the shape preserves distance between points, and preserves the angle measure of the lines.

      (19 votes)

  • Barilugbene261

    5 years agoPosted 5 years ago. Direct link to Barilugbene261's post “How do change figure acr...”

    How do change figure across the y-axis

    (5 votes)

    • Polina Vitić

      5 years agoPosted 5 years ago. Direct link to Polina Vitić's post “To "*reflect*" a figure a...”

      Determining reflections (video) | Khan Academy (8)

      To "reflect" a figure across the y-axis, you want to do two things. For each of the figure's points:
      - multiply the x-value by -1
      - keep the y-value the same

      For instance, Triangle ABC (in the video) has the following three points:
      A (2, 6)
      B (5, 7)
      C (4, 4)

      To reflect Triangle ABC across the y-axis, we need to take the negative of the x-value but leave the y-value alone, like this:

      A (-2, 6)
      B (-5, 7)
      C (-4, 4)

      * Please note that the process is a bit simpler than in the video because the line of reflection is the actual y-axis. If the line of reflection was something else (like x = -4), you would need to do more than just taking the negative of the x-value - the process would be similar to what Sal does in the video.

      Hope this helps!

      (16 votes)

  • Mohammad Zayd

    5 years agoPosted 5 years ago. Direct link to Mohammad Zayd's post “I have a question. To fin...”

    I have a question. To find the line of reflection for a triangle, could someone count all the spaces between the two same vertices and then divide them by two. Then add that quotient to a vertice. One example could be in the video. The distance between Triangle ABC's vertice of C and Triangle A'B'C''s vertice of C is six. So then divide six by two to get 3. Then add that 3 to Triangle A'B'C' vertice c's Y-coordinate to get 1. The line of reflection is on the Y-coordinate of 1. Sorry if this was a little confusing. It is difficult to type about Triangle A'B'C' and the different vertices. Sorry.

    (10 votes)

    • Ellie

      5 months agoPosted 5 months ago. Direct link to Ellie's post “Yes, you can do it that w...”

      Yes, you can do it that way, although you probably figured that out by now because it's been 4 years.

      (5 votes)

  • mohidafzal31

    5 years agoPosted 5 years ago. Direct link to mohidafzal31's post “I can't seem to find it a...”

    I can't seem to find it anywhere, but one of the questions in a worksheet given by my teacher, we are asked to:
    Reflect at "y = -x"
    Is there a video or exercise on this that I missed? if not then pls guide me

    (6 votes)

    • mohidafzal31

      5 years agoPosted 5 years ago. Direct link to mohidafzal31's post “*Nevermind, punching y = ...”

      *Nevermind, punching y = -x into desmos gave me the line of reflection!*

      (7 votes)

  • bhudson642

    5 years agoPosted 5 years ago. Direct link to bhudson642's post “Why is there nothing on d...”

    Why is there nothing on dilation in this playlist? It's the only type of transformation not covered,

    (5 votes)

  • Aryanna Cortez

    2 years agoPosted 2 years ago. Direct link to Aryanna Cortez's post “Do you know any tricks or...”

    Do you know any tricks or like an easier way to find reflections?

    (3 votes)

    • The Telepath

      2 years agoPosted 2 years ago. Direct link to The Telepath's post “I use a memorization tric...”

      I use a memorization trick. Let's say you are given the point (2, -7).
      To reflect across the x-axis, use the rule (x, -y). This will give you (2, 7).
      To reflect across the y-axis, use the rule (-x, y). This gives you (-2, -7).
      To reflect across the line y=x, use the rule (y, x). This gives you (-7, 2).
      To reflect across the line y=-x, use the rule (-y, -x). This gives you (7, -2).

      Just memorize these formulas and you'll be good. You don't have to graph a point to find its reflection point.

      Hope this helps :D

      (7 votes)

  • zaksab1

    a year agoPosted a year ago. Direct link to zaksab1's post “i didn't understand”

    i didn't understand

    (3 votes)

    • joshua

      a year agoPosted a year ago. Direct link to joshua's post “Please specify what you d...”

      Please specify what you didn't understand. To do reflection for a shape, simply reflect each point respectively, last connect it, forming the reflected shape.

      To know where do you place the reflected point, simply count how many unit(s) is there from that initial point to the line of reflection. Then place the point on the other side of the line of reflection with the same number of unit(s).

      (5 votes)

  • Anderson Adoral

    a year agoPosted a year ago. Direct link to Anderson Adoral's post “what if the line of refle...”

    what if the line of reflection os oblique? is there a general rule for the points?

    (3 votes)

    • Venkata

      a year agoPosted a year ago. Direct link to Venkata's post “One thing you could do is...”

      One thing you could do is this: Consider the point given and the line of reflection (which is oblique). Now, draw a line from the point till you intersect the line of reflection. After you intersect it, draw a line perpendicular to the line you just drew, but make sure that this line is equal in length to the first line. Where your second line stops is the reflection of the point.

      Observe that the idea here is to make a square with the point as one corner and the line of reflection as the diagonal.

      (5 votes)

  • Anna Maxwell

    4 years agoPosted 4 years ago. Direct link to Anna Maxwell's post “So was that reflection a ...”

    So was that reflection a reflection across the y-axis?

    (2 votes)

    • Odelia

      4 years agoPosted 4 years ago. Direct link to Odelia's post “No, It would be a reflect...”

      No, It would be a reflection across something on the x-axis.
      Hope that helps!

      (5 votes)

  • MartiW

    10 months agoPosted 10 months ago. Direct link to MartiW's post “the dang volume isn't wor...”

    the dang volume isn't working, so, I am confused on what's happening. Please help me with this!

    (2 votes)

    • Storm_0891

      10 months agoPosted 10 months ago. Direct link to Storm_0891's post “Sal was just attempting t...”

      Sal was just attempting to find the where the line of reflection is at. He found it, then checked his work with the points by counting how many units away they were from the line.

      (3 votes)

Video transcript

- [Instructor] We're asked todraw the line of reflection that reflects triangle ABC,so that's this blue triangle, onto triangle A prime B prime C prime, which is this redtriangle right over here. And they give us alittle line drawing tool in order to draw the line of reflection. So the way I'm gonna think about it is well, when I just eyeball it, it looks like I'm just flipped over some type of a horizontal line here. But let's see if we can actually construct a horizontal line whereit does actually look like the line of reflection. So let's see, C and C prime, how far apart are they from each other? So if we go one, two,three, four, five, six down. So they are six apart. So let's see if we just putthis three above C prime and three below C, let's seeif this horizontal line works as a line of reflection. So C, or C prime isdefinitely the reflection of C across this line. C is exactly three units above it, and C prime is exactlythree units below it. Let's see if it works for A and A prime. A is one, two, three,four, five units above it. A prime is one, two, three,four, five units below it. So that's looking good. Now let's just check out B. So B, we can see it's at they-coordinate here is seven. This line right over hereis y is equal to one. And so what we wouldhave here is, let's see, this looks like it's sixunits above this line, and B prime is six units below the line. So this indeed works. We've just constructedthe line of reflection that reflects the bluetriangle, triangle ABC, onto triangle A prime B prime C prime.

Determining reflections (video) | Khan Academy (2024)

FAQs

How to determine reflections? ›

To reflect over the x-axis, change the sign on the y coordinates of selected given points. Reflections over the y-axis require the x coordinated to be negated. Reflections over the origin require that both the x and y coordinates be negated, and to reflect over the line y=x, swap x and y.

Who is the guy in Khan Academy videos? ›

Salman "Sal" Amin Khan (born October 11, 1976) is an American educator and the founder of Khan Academy, a free online non-profit educational platform with which he has produced over 6,500 video lessons teaching a wide spectrum of academic subjects, originally focusing on mathematics and science.

How to find the line of reflections? ›

A line of reflection is an imaginary line that flips one shape onto another. We find this line by finding the halfway points between matching points on the source and image triangles. All of the halfway points are on the line. Once we find that line, it shows how one triangle reflects onto the other.

How does Khan Academy record their videos? ›

Khan academy uses a OBS software to record the screen combined with a digital whiteboard software which has the interface to draw and write and he uses a Drawing Tablet to physically write on it with a stylus with great precision.

What are the 3 reflection rules? ›

  • The angle of reflection is equal to the angle of incidence .
  • The incident ray, the reflected ray and the normal lie in the same plane.
  • The incident ray and the reflected ray are on the opposite sides of the normal.

What is the 4 law of reflection? ›

The law of reflection states that the angle of reflection equals the angle of incidence— θr = θi. The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface. Figure 2.

What is Sal Khan's salary? ›

31-year-old Sal Khan earns $220,000 a year and saves 75% of his salary by living with his parents: "I'm grateful for this choice." Tap the link in bio to learn why he chose to live at home, and to see how he spends his money.

What is Sal Khan's religion? ›

He is a Bengali-American and a Muslim.

Where did Sal Khan go to college? ›

Khan attended the prestigious Massachusetts Institute of Technology where he received a bachelor's degree in math and a master's degree in computer science. Armed with his degrees and an excellent work ethic, he then set out to work as a hedge fund analyst.

Is there a formula for reflection? ›

A reflection is a transformation representing a flip of a point, curve, or some figure. The two primary reflections covered in this lesson are: Reflection over x-axis: This is a reflection or flip over the x-axis where the x-axis is the line of reflection used. The formula for this is: ( x , y ) → ( x , − y ) .

What is b in y mx b? ›

In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.

How do you calculate the number of reflections? ›

Let d equal the horizontal distance traveled by the light between reflections off either mirror. Calculate the distance d by multiplying the separation distance by the tangent of the beam angle. Divide the total distance (168 cm) by d to calculate the total number of reflections.

How does Khan Academy make money? ›

Khan Academy is a 501(c)(3) non-profit organization, mostly funded by donations from philanthropic organizations. On its IRS form 990, the organization reported $31 million in revenues in 2018 and $28 million in 2019, including $839,000 in 2019 compensation for Khan as CEO.

Can teachers see what you do on Khan Academy? ›

Khan Academy offers teachers insight to track their students' work on both assigned and unassigned content.

Is Khan Academy paid? ›

Education is a human right. We are a nonprofit because we believe in a free, world-class education for anyone, anywhere. Instead of ads or subscriptions, we are supported by individual contributions from people like you. Please join us today.

What is the formula for calculating reflection? ›

Reflection over Y = X

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). The reflection of the point (x, y) across the line y = – x is (-y, -x).

How do you tell if a function has a reflection? ›

When reflecting over the x-axis, the function f(x) becomes -f(x). For instance, y = 3x^2 would become y = -(3x^2). On the other hand, when we reflect the function f(x) over the y-axis it becomes f(-x). For instance y = 3x^2 + 2x would become y = 3(-x^2) + 2(-x).

How to find the reflection of a point? ›

Find the intersection point of the given line and the perpendicular bisector. This point is the center of reflection. Use the center of reflection to calculate the distance between the given point and the center. Reflect the point across the center using the distance and direction.

How do you identify reflection symmetry? ›

Step 1: On each side of the line of symmetry, determine the distance from each vertex/side to the line of symmetry. Step 2: Determine whether the figure has reflective symmetry. If the corresponding vertices/sides are an equal distance to the line of symmetry, then the figure has reflective symmetry.

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