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/translating-points 2023-05-12T21:01:01.897246564Z Translating points Let's practice translations on a coordinate plane. A translation is a way to move a point or shape by a certain number of units in a certain direction. For example, we can translate a point by moving it 5 units left and 3 units up. We describe this translation algebraically using the coordinates (x-5, y+3). video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Translating points Let's practice translations on a coordinate plane. A translation is a way to move a point or shape by a certain number of units in a certain direction. For example, we can translate a point by moving it 5 units left and 3 units up. We describe this translation algebraically using the coordinates (x-5, y+3). https://cdn.kastatic.org/ka-youtube-converted/SxxzfojT1Pw.mp4/SxxzfojT1Pw.mp4 231 Translations, reflections and rotations in the Cartesian plane 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/v/formal-translation-tool-example 2023-05-12T21:01:01.897246564Z Determining translations We can find the translation by figuring out how much the x- and y-coordinates need to change to map one triangle onto the other. We map each point to its corresponding point in the other triangle. Moving left means the translation of x is negative, and moving down means the translation of y is negative. video https://cdn.kastatic.org/googleusercontent/MPuyrjMLnt3OZPtKYxV7UDofpeveprlz-qdahgIRmt_VeRed9JpWtBAVQhhA3KXelDtCaDJaC1kXiH2_nG9c_dN9Iw Determining translations We can find the translation by figuring out how much the x- and y-coordinates need to change to map one triangle onto the other. We map each point to its corresponding point in the other triangle. Moving left means the translation of x is negative, and moving down means the translation of y is negative. https://cdn.kastatic.org/ka-youtube-converted/BrYEuO7fwMw.mp4/BrYEuO7fwMw.mp4 92 Translations, reflections and rotations in the Cartesian plane https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/a/determining-translations 2025-09-27T00:00:43.070802795Z Determining translations Learn how to find the necessary translation to map a given source shape onto a given image shape. article https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/e/defining-translations 2022-05-11T21:30:48.428428457Z Determine translations Given two figures on the coordinate plane, find the formal definition of the translation that takes one figure to another. 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 Translations, reflections and rotations in the Cartesian plane 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/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 Translations, reflections and rotations in the Cartesian plane 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-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 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 Translations, reflections and rotations in the Cartesian plane 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/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 Translations, reflections and rotations in the Cartesian plane 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/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