https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/a/intro-to-translations 2022-06-13T22:23:00.945663613Z Translations intro Learn what translations are and how to perform them in our interactive widget. article https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/v/drawing-image-of-translation 2023-05-12T21:01:01.897246564Z Translating shapes In translations, we slide a shape around on a grid. We use the letter "T" to represent translations. We move every point of the shape a certain distance left or right, and up or down, to create a new shape that's the same size and shape as the original. We call the new shape the image. video https://cdn.kastatic.org/googleusercontent/ySKQzBpik5dGcZ--I_GUQ07IzW38o_zK2VXJkdCCwnE9R2xiLor1miZwbXMOXOYGG-7BAOeyu1UwcvbWjLvMYEWj Translating shapes In translations, we slide a shape around on a grid. We use the letter "T" to represent translations. We move every point of the shape a certain distance left or right, and up or down, to create a new shape that's the same size and shape as the original. We call the new shape the image. https://cdn.kastatic.org/ka-youtube-converted/g_ijRF_NMLk.mp4/g_ijRF_NMLk.mp4 115 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/e/performing-translations-on-the-coordinate-plane 2026-04-29T23:30:31.829809381Z Translate points Given a point and a definition of a translation, plot the translation on a coordinate plane or identify the coordinates of the translated point. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/e/translations 2026-04-08T01:15:04.085520103Z Translate shapes Given a figure and a definition of a translation, manually draw the image. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/geometric-transformations/translations-8th/a/translations-review 2023-12-11T22:13:00.981327266Z Translations review Review the basics of translations, and then perform some translations. article https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-transformation-properties-and-proofs/hs-geo-symmetry/v/axis-of-symmetry 2021-06-30T20:49:36Z Intro to reflective symmetry Introduction to the concept of an "axis of symmetry" Sal Khan video https://cdn.kastatic.org/googleusercontent/RX22YtkIO09r8CTvJ3jTdp0j9E8aE-4NaE_FdQbNSyGk6MP49fxOTEHnX4tX4eOfH6wT8gsXpSCV-F8Q2fmkgnmW Intro to reflective symmetry Introduction to the concept of an "axis of symmetry" https://cdn.kastatic.org/ka-youtube-converted/LrTn4cvsewk.mp4/LrTn4cvsewk.mp4 167 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-transformation-properties-and-proofs/hs-geo-symmetry/e/symmetry-of-two-dimensional-shapes 2024-03-11T03:39:15.267265986Z Reflective symmetry of 2D shapes Analyze various shapes according to their reflective symmetries. Tomer Gal exercise 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 Translation, reflection and rotation with shapes 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/geometry/hs-geo-transformations/hs-geo-reflections/v/reflecting-points 2023-05-12T21:01:01.897246564Z Reflecting points We can plot points after reflecting them across a line, like the x-axis or y-axis. Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right.  video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Reflecting points We can plot points after reflecting them across a line, like the x-axis or y-axis. Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right.  https://cdn.kastatic.org/ka-youtube-converted/F77xiSlCehI.mp4/F77xiSlCehI.mp4 225 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/e/performing-reflections-on-the-coordinate-plane 2026-04-08T00:36:09.500768563Z Reflect points Given a point and a definition of a horizontal or vertical reflection, plot the reflection on a coordinate plane or identify the coordinates of the reflected point. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/v/reflecting-shapes 2023-05-12T21:01:01.897246564Z Reflecting shapes Let's reflect a quadrilateral across the x-axis. To do this, we find new points (A', B', C', D') by keeping the same x-coordinates and changing the y-coordinates to their opposite signs. This creates a flipped image of the original quadrilateral. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Reflecting shapes Let's reflect a quadrilateral across the x-axis. To do this, we find new points (A', B', C', D') by keeping the same x-coordinates and changing the y-coordinates to their opposite signs. This creates a flipped image of the original quadrilateral. https://cdn.kastatic.org/ka-youtube-converted/lfBDOQddTD0.mp4/lfBDOQddTD0.mp4 158 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/e/reflections-1 2026-04-07T23:17:37.123726494Z Reflect shapes Given a figure and a definition of a reflection, manually draw the image. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-reflections/a/reflecting-shapes 2022-05-10T22:02:00.85367701Z Reflecting shapes Learn how to find the image of a given reflection. article https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-transformation-properties-and-proofs/hs-geo-symmetry/v/example-rotating-polygons 2021-02-16T16:08:13Z Intro to rotational symmetry Sal checks whether various figure are symmetrical under a 180 degrees rotation. Sal Khan video https://cdn.kastatic.org/googleusercontent/sjvgJaDero2jqNHDjxN-uzBv5YH0m-lNVi5mvuC-MjglbNRSb3wvcN30eVZYHAo5Y_EEdm0jBKuhW4EB_T8CRvY6 Intro to rotational symmetry Sal checks whether various figure are symmetrical under a 180 degrees rotation. https://cdn.kastatic.org/ka-youtube-converted/P35LyN9g0oI.mp4/P35LyN9g0oI.mp4 248 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-transformation-properties-and-proofs/hs-geo-symmetry/e/rotational-symmetry-of-2d-shapes 2026-03-31T08:44:48.259988263Z Rotational symmetry of 2D shapes Identify rotational symmetry in figures by determining magnitudes of rotations which map a figure onto itself. Charlotte Auen exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/v/rotating-points 2023-05-12T21:01:01.897246564Z Rotating points Positive rotation angles mean we turn counterclockwise. Negative angles are clockwise. We can think of a 60 degree turn as 1/3 of a 180 degree turn. A 90 degree turn is 1/4 of the way around a full circle. The angle goes from the center to first point, then from the center to the image of the point. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Rotating points Positive rotation angles mean we turn counterclockwise. Negative angles are clockwise. We can think of a 60 degree turn as 1/3 of a 180 degree turn. A 90 degree turn is 1/4 of the way around a full circle. The angle goes from the center to first point, then from the center to the image of the point. https://cdn.kastatic.org/ka-youtube-converted/0NYbQPcdxg8.mp4/0NYbQPcdxg8.mp4 110 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/cc-eighth-grade-math/geometric-transformations/rotations-8th/e/rotate-points--basic- 2026-06-30T22:20:38.649299897Z Rotate points (basic) Given a point and a definition of a rotation, plot the rotation on a coordinate plane or identify the coordinates of the rotated point.  Rotations are about the origin and multiples of 90º. Lindsay exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/v/points-after-rotation 2021-02-16T16:08:13Z Rotating shapes Sal is given a triangle on the coordinate plane and the definition of a rotation about the origin, and he manually draws the image of that rotation. video https://cdn.kastatic.org/googleusercontent/ryzpJhKhWrS1aIVhgEGBk4l1pSuU5cwCYGGk3g3Z_n65H4DZIhy6iKwT75LvrxuldQ4_i68sddB0kyK07XCJhwN3 Rotating shapes Sal is given a triangle on the coordinate plane and the definition of a rotation about the origin, and he manually draws the image of that rotation. https://cdn.kastatic.org/ka-youtube-converted/6nUMiJfHLSA.mp4/6nUMiJfHLSA.mp4 492 Translation, reflection and rotation with shapes https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/e/rotations-1 2026-04-07T23:36:17.218592739Z Rotate shapes Given a figure on the coordinate plane and the definition of a rotation about the origin, manually draw the image of that rotation. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/a/intro-to-rotations 2022-06-13T22:23:00.945663613Z Rotations intro Learn what rotations are and how to perform them in our interactive widget. article