An Isometry is a transformation that preserves length. What is an Isometry? An Isometry is a transformation that preserves length.

What transformations are Isometries? Type Diagram A translation moves a figure left, right, up, or down Preimage Image A reflection moves a figure across its line of reflection to create its mirror image. A rotation moves a figure around a given point.

Translation/ how to Find point A and Translate ABC according to the rule (x,y) (x+6,y) Find point A and Find point B and Find point C and 6 Units A A’ count 6 units to the right. Plot point A’. B’ B C C’ count 6 units to the right. Plot point B’. count 6 units to the right. Plot point C’.

Translation Rules To the right: Add to the X-coordinate To the left: Subtract from the X-coordinate Up: Add to the Y-coordinate Down: Subtract from the Y-coordinate

9 units to the right and 5 units down Translation example: Translate point P (3, 2) according to the rule <X+9, Y-5> 9 units to the right and 5 units down Add 3 to the x-coordinate. 3 + 9 = 12 Subtract 5 from the y-coordinate. 2 – 5 = -3 Therefore the coordinates of the image P’ are (12, -3)

Reflection / how to Reflect ABC across the y-axis. Count the number of units point A is from the line of reflection. 5 Units 5 Units A A’ Count the same number of units on the other side and plot point A’. 2 Units 2 Units B B’ 3 Units 3 Units Count the number of units point B is from the line of reflection. C C’ Count the same number of units on the other side and plot point B’. Count the number of units point C is from the line of reflection. Count the same number of units on the other side and plot point C’.

Reflection Rules Over the X-axis: Over the Y-axis: Change sign for Y-coordinate Over the Y-axis: Change sign for X-coordinate

Reflection Rules Over line Y=X: Switch x and y coordinates Over Line Y= -X: Change sign for y-coordinate AND change signs Over line Y=X: Switch x and y coordinates

Reflection practice The coordinates of ABC are: (-5, -4), (-2, 3), (3, 1) Reflect ABC across the y-axis and then reflect it across the x-axis. To reflect it across the y-axis just change the sign for x. The new coordinates are: (5, -4), (2, 3), (-3, 1) To reflect it across the x-axis keep the x the same and change sign for y. The new coordinates are: (-5, 4), (2, -3), (-3, -1)

Switch the x and y coordinates: Reflection practice The coordinates of ABC are: (-5, -4), (-2, 3), (3, 1) Reflect ABC across the line Y= -X Switch the x and y coordinates: (-4, -5), (3, -2), (1, 3) 2. Change the signs (+4, +5), (-3, +2), (-1, -3)

STOP HERE We will cover rotations on Monday during class.

Rotate  ABO 180° about the origin. Rotation Rules To rotate a point 180°, just change the signs for both coordinates. Rotate  ABO 180° about the origin. A (2, 4) A’ (-2, -4) B (5, 1) B’ (-5, -1) O (0, 0) O’ (0, 0)

Rotation Rules To rotate a point 90° or 270° switch the x and y coordinates AND add look up signs on coordinate plane: (2, 5) Rotate point P (5, -2) 90° counter clock wise 1) Switch x and y: (-2, 5) (5, -2) 2) The image should be in quadrant I where both signs are POSITIVE therefore P’ = (2, 5)

Rotation Rules To rotate a point 90° or 270° switch the x and y coordinates AND add look up signs on coordinate plane: Rotate point M (-1, -3) 270° clock wise 1) Switch x and y: (-3, -1) (3, -1) (-1 , -3) 2) The image should be in quadrant IV where X is positive and y is negative then M’ = (3, -1)

Rotations practice Point P (5, 8). Rotate 270° clockwise about the origin. Point Z (-3, -6). Rotate 180° about the origin. Rotate LMN, with coordinates L(3, 6), M(5, 9), N (7, 12), 90° clockwise about the origin. P’ (-8, 5) Z’ (-3, -6) L’M’N’ (6, -3), (9, -5), (7, -12)

Practice A 270° clockwise rotation about the origin is the same as… Rotate point P (-3, 7) 90° counter clock wise about the origin A 90° counter clock wise rotation A 270° counter clock wise rotation P’ = ( -7, -3)