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 Understanding geometric transformations https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/v/identifying-transformations 2023-05-12T21:01:01.897246564Z Identifying transformations Let's look at four types of transformations: rotations (spinning a shape around a point), translations (shifting a shape), reflections (flipping a shape over a line), and dilations (shrinking or expanding a shape). We practice identifying these transformations in different pairs of figures. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Identifying transformations Let's look at four types of transformations: rotations (spinning a shape around a point), translations (shifting a shape), reflections (flipping a shape over a line), and dilations (shrinking or expanding a shape). We practice identifying these transformations in different pairs of figures. https://cdn.kastatic.org/ka-youtube-converted/K7QTjFdUIyk.mp4/K7QTjFdUIyk.mp4 227 Understanding geometric transformations https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/v/determining-reflections 2023-05-12T21:01:01.897246564Z Determining 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. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Determining 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. https://cdn.kastatic.org/ka-youtube-converted/435Ipnmp7bA.mp4/435Ipnmp7bA.mp4 100 Understanding geometric transformations https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/v/defining-rotation-example 2023-05-12T21:01:01.897246564Z Determining rotations To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. Counterclockwise rotations have positive angles, while clockwise rotations have negative angles. Then we estimate the angle. For example, 30 degrees is 1/3 of a right angle. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Determining rotations To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. Counterclockwise rotations have positive angles, while clockwise rotations have negative angles. Then we estimate the angle. For example, 30 degrees is 1/3 of a right angle. https://cdn.kastatic.org/ka-youtube-converted/6pH-7pciYU8.mp4/6pH-7pciYU8.mp4 177 Understanding geometric transformations 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 Understanding geometric transformations 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 Understanding geometric transformations https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/a/determining-rotations 2023-09-29T20:10:37.268517027Z Determining rotations Learn how to determine which rotation brings one given shape to another given shape. article https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/e/determine-reflections 2025-11-21T17:50:47.901900147Z Determine reflections Given a shape and its image under a horizontal or vertical reflection, determine the line of reflection. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/geometric-transformations/rotations-8th/e/determine-rotations--basic- 2023-12-11T22:13:00.981327266Z Determine rotations (basic) Given a figure on the coordinate plane and a center of a rotation, find the angle for the rotation that maps one figure to the other.  Rotations are around the origin and a multiple of 90º. Lindsay exercise 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