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2 -2 4 -4 2 -2 4 -4 6 -6 . . . . . When (x,y) is rotated 180 degrees about the origin, its new image is: . . . . . ( -x,-y ) C' . . . A' . . B' . . . . . . . . . . . . . . . . . . . . . . . . A (4,4) → A' (-4,-4) B (3,1) → B' (-3,-1) C (5,1) → C' (-5,-1) . . . . . B . A . . C . . . . . . . . . . 2 -2 4 -4 2 -2 4 -4 6 -6 When you rotate a point about the origin, The origin is the point of rotation B' A 180 degree rotation about the origin forms a angle (line) When you connect the preimage B and image B' thru the origin B ∘ 2 -2 4 -4 2 -2 4 -4 6 -6 A 90 degree rotation about the origin forms a right angle When you connect the preimage B and image B' thru the origin When you rotate a point about the origin, The origin is the point of rotation ∘ B' B 2 -2 4 -4 2 -2 4 -4 6 -6 Each time you rotate a point 180 degrees about the origin, BOTH the x and coordinates change sign (-3,-1) B' Each time you rotate a point 360 degrees about the origin, the x and y coordinates remain the SAME B (3,1) 2 -2 4 -4 2 -2 4 -4 6 -6 Rotation: 0 (none) 180 360 Location: (-3,-1) (3,1) B' (-3,-1) B (3,1) (3,1) Click OK 2 -2 4 -4 2 -2 4 -4 6 -6 (-5,-1) Rotation: 0 (none) 180 360 Location: B' (5,1) ( , ) ( , ) B (5,1) 2 -2 4 -4 2 -2 4 -4 6 -6 Rotation: 0 (none) 90 180 Location: (-3,-1) . (3,1) (1,-3) . . (-3,-1) B' (1,-3) B . (3,1) . Click on the 90 degree rotation Rotation: 0 90 180 270 360 Location: The pattern for 90 degree rotations about the origin is similar to connecting dominoes.... (3,1) (1,-3) ◠ ◡ (-3,-1) (-1,3) (3,1) Rotation: 0 90 180 270 360 Location: First, write the points for 180 degree (opposite x and y) and 360 degree (same as original) rotations. (3,1) (-3,-1) (3,1) Then, fill in the blanks (90 and 270 degrees) by connecting matching coordinates. Rotation: 0 90 180 270 360 Location: (3,1) ◡ (1,-3) matching numbers ◡ (-3,-1) ◡ (-1,3) ◡ (3,1) Location Rotation 1. To rotate the original image point (2,5) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. (2,5) 0 90 180 270 360 (-2,-5) ? (2,5) ? Location Rotation 1. 2. To rotate the original image point (2,5) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. Fill in the 90 and 270 degree rotations by connecting matching coordinates. (2,5) 0 90 180 270 360 (5,-2) ? (-2,-5) (-5,2) ? (2,5) Location Rotation (2,5) 0 90 180 270 360 ◡ connect 5 and 5 (5,-2) connect -2 and -2 ◡ (-2,-5) connect -5 and -5 ◡ (-5,2) ◡ connect 2 and 2 (2,5) Location Rotation 1. To rotate the original image point (4,3) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. (4,3) 0 90 180 270 360 (-4,-3) ? (4,3) ? Location Rotation 1. 2. To rotate the original image point (4,3) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. Fill in the 90 and 270 degree rotations by connecting matching coordinates. (4,3) 0 90 180 270 360 (3,-4) ? (-4,-3) (-3,4) ? (4,3) Location Rotation 1. 2. To rotate the original image point (7,-5) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. Fill in the 90 and 270 degree rotations by connecting matching coordinates. (7,-5) 0 90 180 270 360 (-5,-7) ? (-7,5) ? (5,7) ? (7,-5) ? Location Rotation 1. 2. To rotate the original image point (-6,-8) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. Fill in the 90 and 270 degree rotations by connecting matching coordinates. (-6,-8) 0 90 180 270 360 (-8,6) ? (6,8) ? (8,-6) ? (-6,-8) ? Location Rotation 1. 2. To rotate the original image point (-4,9) about the origin: Fill in the points for a 180 degree (opposite) and 360 degree (same as original) rotation. Fill in the 90 and 270 degree rotations by connecting matching coordinates. (-4,9) 0 90 180 270 360 ( 9,4) ? (4,-9) ? (-9,-4) ? (-4,9) ? The End |