https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/v/introduction-to-transformations 2023-05-12T21:01:01.897246564Z Rigid transformations intro Transformations in math involve changing a shape's position or which way the shape points. There are three main types: translations (moving the shape), rotations (turning the shape), and reflections (flipping the shape like a mirror image). Rigid transformations keep the shape's size and angles the same. The image is the shape in its new position and direction. video https://cdn.kastatic.org/googleusercontent/N7hCRdFMymh36aIKEaMUOfM717F6tWCMcIqdHYv1A1t8iFQk_MwtL3EIkag2-3ZOwvcGgHgbBB_vL6nhPc_SnpeS Rigid transformations intro Transformations in math involve changing a shape's position or which way the shape points. There are three main types: translations (moving the shape), rotations (turning the shape), and reflections (flipping the shape like a mirror image). Rigid transformations keep the shape's size and angles the same. The image is the shape in its new position and direction. https://cdn.kastatic.org/ka-youtube-converted/XiAoUDfrar0.mp4/XiAoUDfrar0.mp4 443 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/v/dilations-intro 2023-05-12T21:01:01.897246564Z Dilations intro Dilations are a type of non-rigid transformation. They change the size of a shape by scaling it up or down, making it bigger or smaller. Unlike rigid transformations, dilations do not keep the shape's size the same. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Dilations intro Dilations are a type of non-rigid transformation. They change the size of a shape by scaling it up or down, making it bigger or smaller. Unlike rigid transformations, dilations do not keep the shape's size the same. https://cdn.kastatic.org/ka-youtube-converted/Kv-lyVmQ5ps.mp4/Kv-lyVmQ5ps.mp4 91 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-points-example 2023-05-12T21:01:01.897246564Z Dilating points 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. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Dilating points 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. https://cdn.kastatic.org/ka-youtube-converted/N0_HfmxdbCg.mp4/N0_HfmxdbCg.mp4 187 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/e/performing-dilations 2026-04-08T00:16:02.937952483Z Dilate points Use the interactive transformation tool to perform dilations. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilation-scale-factor 2023-05-12T21:01:01.897246564Z Dilations: scale factor Dilations make a shape bigger or smaller. A scale factor tells us how much to multiply by the side lengths to change the size. The scale factor is the ratio of the side length in the new shape (image) to the side length in the corresponding side in the original shape (pre-image). Each pair of corresponding sides has the same factor. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Dilations: scale factor Dilations make a shape bigger or smaller. A scale factor tells us how much to multiply by the side lengths to change the size. The scale factor is the ratio of the side length in the new shape (image) to the side length in the corresponding side in the original shape (pre-image). Each pair of corresponding sides has the same factor. https://cdn.kastatic.org/ka-youtube-converted/b4ORXN7a0-w.mp4/b4ORXN7a0-w.mp4 299 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/e/defining-dilations-2 2026-03-25T12:10:34.88329628Z Dilations: scale factor Find both the center and the scale factor of a dilation that maps a given figure to another one. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/example-identifying-the-center-of-dilation 2021-02-07T17:14:01Z Dilations: center Determining the center of dilation, given a figure and its image under a dilation. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Dilations: center Determining the center of dilation, given a figure and its image under a dilation. https://cdn.kastatic.org/ka-youtube-converted/rDj0WNzp-f8.mp4/rDj0WNzp-f8.mp4 163 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/e/dilations-center 2023-07-03T04:14:08.892509966Z Dilations: center Given a figure and its image under a dilation, determine the dilation's center point. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/thinking-about-dilations 2023-05-12T21:01:01.897246564Z Dilating shapes: expanding Let's dilate a rectangle around a point P using a scale factor 1 2/3. This changes the size of the rectangle while keeping its shape. Because 1 2/3 is bigger than 1, most of the points get farther from P. Point P stays in place, because a distance of 0 times any scale factor is still 0. Sal Khan video https://cdn.kastatic.org/googleusercontent/eJ0ujicJxWleCFPYnHJObwHRlmrxSg4avLuQ3GrdBJHtk4EI_DeMFHol8Dm3vW8BQeZF6FyzfMPhmWyUYGuloJ1v Dilating shapes: expanding Let's dilate a rectangle around a point P using a scale factor 1 2/3. This changes the size of the rectangle while keeping its shape. Because 1 2/3 is bigger than 1, most of the points get farther from P. Point P stays in place, because a distance of 0 times any scale factor is still 0. https://cdn.kastatic.org/ka-youtube-converted/6dyWKD_JPhI.mp4/6dyWKD_JPhI.mp4 159 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-shapes-shrinking 2022-09-10T02:03:40.164764806Z Dilating shapes: shrinking Draw the image of the triangle under a dilation with scale factor 1/4 about the center of dilation on the coordinate plane. video https://cdn.kastatic.org/ka_thumbnails_cache/3c857dc6-945a-4df1-9529-5af882c817de_1280_720_base.png Dilating shapes: shrinking Draw the image of the triangle under a dilation with scale factor 1/4 about the center of dilation on the coordinate plane. https://cdn.kastatic.org/ka-youtube-converted/xAxgxUHzgaY.mp4/xAxgxUHzgaY.mp4 146 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-triangles-find-the-error 2022-09-10T02:03:40.164764806Z Dilating triangles: find the error Dilating doesn't just shrink or grow a figure. The scale factor also changes the distance from each point to the center of dilation. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/9cf2696d-88e8-4663-9a81-0bbe629412ee_1280_720_base.png Dilating triangles: find the error Dilating doesn't just shrink or grow a figure. The scale factor also changes the distance from each point to the center of dilation. https://cdn.kastatic.org/ka-youtube-converted/Kry9Bhp4PQg.mp4/Kry9Bhp4PQg.mp4 161 Homotecia https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/e/dilations 2026-04-08T00:16:02.937952483Z Dilate triangles Given a figure and a definition of a dilation, select or manually draw the image. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-2d-vs-3d/v/dilating-in-3d 2023-05-19T19:08:41.791622529Z Dilating in 3D The cross sections of 3D shapes are dilations of the original shape, centered at a specific point. The scale factor of the dilation depends on the height of the cross-section or the distance from the point on the base.  Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/3d749690-7d86-41c2-b568-58d3b7b26f27_1280_720_base.png Dilating in 3D The cross sections of 3D shapes are dilations of the original shape, centered at a specific point. The scale factor of the dilation depends on the height of the cross-section or the distance from the point on the base.  https://cdn.kastatic.org/ka-youtube-converted/3wTy5aI9AF4.mp4/3wTy5aI9AF4.mp4 273 Homotecia