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- Example: Find the center of dilation if dilating (3, −7) by a factor 3 results in (9, −3). Let (𝑥, 𝑦) be the center of dilation. Then we have 𝑥 = (3 ∙ 3 − 9)∕ (3 − 1) = 0 𝑦 = (3 ∙ (−7) − (−3))∕ (3 − 1) = −9 So, the center of dilation is (0, −9)
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Example: Find the center of dilation if dilating (3, −7) by a factor 3 results in (9, −3). Let (𝑥, 𝑦) be the center of dilation. Then we have 𝑥 = (3 ∙ 3 − 9)∕(3 − 1) = 0 𝑦 = (3 ∙ (−7) − (−3))∕(3 − 1) = −9 So, the center of dilation is (0, −9)
- Dilations: Center
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- Dilating Points
Dilations are a way to stretch or shrink shapes around a...
- Performing dilations (video)
Performing dilations. To dilate a point on a coordinate...
- Dilations: Center
People also ask
How to find the center of dilation?
Why isn't the center of dilation C?
What is the center of dilation if scale factor is greater than 1?
How do you calculate a dilation?
Learn how to find the center of dilation, and see examples that walk through sample problems step-by-step for you to improve your math knowledge and skills.
Dilations are a way to stretch or shrink shapes around a point called the center of dilation. The amount we stretch or shrink is called the scale factor. If the scale factor is greater than 1, the shape stretches. If it's between 0 and 1, the shape shrinks.
- 3 min
- It actually doesn't matter! The key thing is that the dilation value affects the distance between two points. As in the first example (dilation by...
- That's a great question! While a coordinate plane is helpful in making our measurements more exact and accurate, it is by no means necessary. In fa...
- No, unless you’re dilating shapes by a factor that is greater than 1. According to Wikipedia, a shear is “the component of stress coplanar with a m...
- I think the origin is always the coordinate 0,0.
- If the point that you are dilating is directly above the point of dilation and you are dilating by 3, you take the distance from the point of dilat...
- It is called "prime", it's there to say that the point is not the original point, but the image of the original one after transformation. A = origi...
- To get from the point of origin to A. Then divide those by 3 and you have A'. Do you think you can figure out where A' might be? Hope this helps. G...
Performing dilations. To dilate a point on a coordinate plane, you multiply its coordinates by a scale factor. The scale factor is a positive number that tells you how much to enlarge or shrink the point. If the scale factor is greater than 1, the point moves away from the origin.
- 3 min
- Sal Khan
Solved Examples on Dilation in Geometry. Example 1: A triangle ABC with AB = 6, BC = 8, and CA = 10, is dilated by a scale factor of 2 with the center of dilation at the origin. Find the lengths of the corresponding sides in the dilated triangle.
The center of dilation is a fixed point in the coordinate plane where we can measure the distances of a shape’s vertices. For example, we consider the quadrilateral ABCD and the point X which will be our center of dilation:
What is a Dilation? A dilation is a type of transformation that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a picture of each type of dilation (one that gets larger and one that gest smaller). Example 1.
