 You can dilate geometric objects in the Cabri Jr.

The Dilation tool in the in the F4 Transformation menu is used to increase or decrease the size of an object by a factor of k. The dilation of an object also takes place with respect to a fixed point the dilation point. If that point is at the center of the object, such as the center of a circle, the object increases or decreases in size and the center of the object remains fixed.

The distance that the dilated object moves is determined by k. The dilation point can be one of the points on the already constructed object. The first picture shows that the already constructed triangle is to be dilated with respect to a point outside the triangle. Use the Alpha-Num tool in the F5 Appearance menu to place the value of the dilation factor k anywhere on the screen. This is illustrated in the first picture, where the dilation factor is placed in the upper-right corner of the screen.

Cabri Jr. The object to be dilated blinks when the cursor is placed on it. When selecting a triangle or quadrilateral, all sides of the object must be blinking to select the whole object instead of just one side of the object. To do this, place the cursor inside the object and move it slightly until all sides are blinking.

Repeat Steps 3 and 4 to dilate more objects. After dilating objects, if you move the center of dilation, the dilated object moves to the location determined by the new center. Jeff McCalla is a mathematics teacher at St. Edwards is an educator who has presented numerous workshops on using TI calculators. Dilate Geometric Objects in Cabri Jr.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math High school geometry Performing transformations Dilations. Practice: Dilate points. Dilations: scale factor. Practice: Dilations: scale factor. Practice: Dilations: center.

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Dilating shapes: expanding. Dilating shapes: shrinking. Dilating triangles: find the error. Practice: Dilate triangles. Current timeTotal duration Math: 8. Google Classroom Facebook Twitter. What is the scale factor of the dilation? So they don't even tell us the center of the dilation, but in order to figure out the scale factor you just have to realize when you do a dilation, the distance between corresponding points will change according to the scale factor.

So for example we could look at the distance between point A and point B right over here. What is our change in y? Our change in, or even what is our distance? Our change in y is our distance because we don't have a change in x. Well this is one, two, three, four, five, six. So this length right over here is equal to six.

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Now what about the corresponding side from A' to B'? Now you might be saying okay that was pretty straightforward because we had a very clear, you could just see the distance between A and B. How would you do it if you didn't have a vertical or a horizontal line? Well one way to think about it is, the changes in y and the changes in x would scale accordingly. So if you looked at the distance between point A and point E, our change in y is negative three right over here, and our change in x is positive three right over here.

Let's do another example. So they're giving us our scale factor. What is the length of segment A'E'? So as I was mentioning while I read it, they didn't actually draw this one out.

So how do we figure out the length of a segment? Well I encourage you to pause the video and try to think about it. So to figure out the length of segment A'E', this is going to be, you could think of it as the image of segment AE. And so you can see that the length of AE is equal to two. Well it is going to be equal to five, five of these units right over here. In fact they haven't even given us enough information.New coordinates by rotation of points Calculator.

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Math Geometry all content Transformations Dilations. Performing dilations. Dilating shapes: expanding. Practice: Dilate points. Practice: Dilations: scale factor. Practice: Dilations: center. Practice: Dilate triangles. Practice: Dilations and properties. Next lesson. Current timeTotal duration Math: HSG. Google Classroom Facebook Twitter. Video transcript Perform a dilation on the coordinate plane. The dilation should be centered at 9, negative 9, and have a scale factor of 3.

So we get our dilation tool out. We'll center it-- actually, so it's already actually centered at 9, negative 9. We could put this wherever we want, but let's center it at 9, negative 9.

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And we want to scale this up by 3. So one way to think about it is, pick any of these points right over here, and they're going to have to get 3 times further away from our center of dilation. So for example, this point C-- actually let's think about these points where they actually want us to fill something in. So point A right over here, it is at the point 4, negative 3. So in the x direction, it is 5 less than 9. We want it to be 3 times further than 9. So we want it to be 15 less than 9.

So we want the x-coordinate of A, 9 minus 15 is negative 6. We want it to go to negative 6. And likewise, we want its y-coordinate to be 3 times further. So right now, let's see, it is at negative 3 relative to negative 9, so it is 6 more on the y direction. We want it to be 18 more. So point A should map to negative 6 comma 9.

And that should give us enough information to just make sure that we are dilating up by a factor of 3. So let's see. Let's dilate up by a factor of 3. So we want to get the image of point A to the point negative 6 comma 9.

So we are there. There we go.Einstein started it all with the theory of relativity. Since then, scientists have conducted many studies and experiments to demonstrate his theory.

Simply defined, time dilation is a difference in the elapsed time measured by two observers. The difference is either due to a velocity difference relative to each other or if the individuals are differently situated relative to a gravitational field.

It would take a lot of time and effort to calculate time dilation.

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Fortunately, you have this time dilation calculator which can assist in getting a better understanding of relativistic effects and of the time dilation formula. Although the concept of time dilation seems confusing to a lot of people, using this dilation calculator is very simple.

As long as you have the values required by the online tool, you can easily get the result you need. Here are the steps for using this speed of light time dilation calculator:. If you plan to use this time dilation calculator, you should understand the concept first. The principle of time dilation claims that time is not experienced in an exact way by everybody. For instance, if you were to move at an extremely high speed, time will slow down. It means that you perceive time passing slower for everything you move relative to.

For a manual calculation of time dilation, use this formula:. This is the very reason behind the counterintuitive nature of relativistic effects.

It also means that we will not be able to experience these effects. Again, if you want to calculate time dilation without having to perform the manual computation, you can use this dilation calculator or speed of light time dilation calculator. Time dilation is a very simple occurrence and can only happen if the speed of light is the same for everyone in the same media.

What you experience with time will remain constant even as you experience a change in speed. However, the relation of your time with those that you leave behind will change.

Trips conducted by astronauts have demonstrated this when their clocks moved slower in direct relation to their speed while leaving Earth. Time does not really exist but is just a representation of motion.This website uses cookies to ensure you get the best experience.

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Determining the scale factor of two quadrilaterals

Please pick an option first What is Given a.Notice that every coordinate of the original triangle has been multiplied by the scale factor x 2. In this problem, the center of the dilation is NOT at the origin. Dilations and Similarity: The term similar or similarity can be defined using the language of transformations. Transformations: Dilations MathBitsNotebook. Dilations are enlargements or reductions! A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

It expands. It contracts. The word " dilate " is often heard in relation to the human eye. Dilations can be seen, in a variety of situations:. School or holiday picture packages offer the same photograph in a variety of sizes, from large to medium to small wallet size photos. Russian nesting dolls are a set of wooden dolls of decreasing size placed inside one another.

After the smallest doll, each doll is an enlargement of its inside doll. The zoom feature will enlarge or reduce the viewing window.

Soft drink containers come in a variety of sizes. While some are of different shapes, others are simply enlargements. Product logos can come in a variety of sizes, such as these pizza shop logos on their small, medium and large boxes. Some grow quickly, while others grow over several days.

Dilations in the coordinate plane: Most dilations in the coordinate plane use the origin, 0,0as the center of the dilation. The center of the dilation will be indicated within the problem or within the notation.

Dilation scale factor Dilation with scale factor 2, multiply by 2. Center at the origin. Dilation not at origin:. Notice that point A and its image are the same. You must observe the distances from the center of the dilation at point A to the other points B, C and D.

Now, draw the image rectangle. For a dilation not at the origin, measure the distances. Two figures are similar if one is the image of the other under a transformation from the plane into itself that multiplies all distances by the same positive scale factor. That is to say, one figure is a dilation of the other. For calculator help with transformations click here. NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.