Transformations and the Coordinate Plane

(+,+) (+,-) (-,-) (-,+) I III IV II Do you remember the QUADRANTS? Do you remember the SIGNS for each Quadrant?

TRANSLATION When you are translating (sliding) a figure right or left, you adjust the x value. When you are translating a figure up or down, you adjust the y value. Move Right = add to x Move Left = subtract from x Move Up = Add to y Move Down = Subtract from y

Give the (x+-,y+-) coordinate for each Translation: 1 to 3 5 to 2 1 to 2 4 to 5 4 to 3 1 to 4 (x + 2, y – 8) (x – 2, y + 3) (x + 7, y) (x, y + 7) (x – 7, y + 2) (x + 9, y – 10)

What if you don’t have graph paper? Translate the following points 5 units to the left and 2 units up: (-4, 2)(0,0)(5, -2)(-3, -5) (-9, 4) Translate 2 units down and 3 units to right: (3, -8)(-2, 3)(0, 5) (-5, 2) (0, 0) (-8, -3) (1, 1) (3, 3)6, -10

Reflection When you reflect across the x-axis, you change the sign of the y value. When you reflect across the y-axis, you change the sign of the x value. When you reflect across the origin (ie y=x or y = -x), you just switch the values and the signs. The x value becomes the y value and the y value becomes the x value. When you reflect across any other line, you just have to make sure your points are equal distance from the reflection line. Remember y = # makes a horizontal line and x = # makes a vertical line.

The trapezoid LMNO is reflected across the x axis. Notice how the numbers change. L (-7, 5) L’ (-7, -5) M (0,5) M’ (0,-5) N (-2,1) N’ (-2, -1) O (-5, 1) O’ (-5, -1) What if we were to reflect LMNO over the y-axis. What would the new coordinates be? L’ (7,5) M’ (0,5) N’ (2,1) O’ (5,1) What if we reflected LMNO over the ORIGIN? L’ (5,-7) M’ (5,0) N’ (1,-2) O’ (1, -5)

No graph paper??? No problem!! We have triangle ABC with the following points: A: (-2,3), B: (5,4), and C: (2, -4) Reflect Triangle ABC across the y-axis……. Reflect Triangle ABC across the x-axis…….. Reflect Triangle ABC across the origin…… A’ (2,3) B’ (-5,4) C’ (-2,-4 A’ (-2,-3) B’ (5,-4) C’ (2, 4) A’ (3,-2) B’ (4,5) C’ (-4,2)

Work Period with partner

Rotations (around origin) Each time you rotate 90° around the origin, you flip the numbers and check your new quadrant. The new quadrant determines the signs of the values. If you rotate 180° around the origin, the numbers stay the same and you check your quadrant for correct sign.

Rotate Triangle ABC 90° clockwise around origin. A (2, 5)……Switch the numbers to get (5,2). Since we are going into quadrant IV, the x will be + and the y will be -. Thus our new point A’ = (5,-2) Using the same rule, what is B’ and C’ B (8,6) B’ (6, -8) C (4,9) C’ (9, -4) A B C Rotate ABC 180° around origin. A (2,5)……Leave the numbers the same to get (2,5). Since we are going into quadrant III, both x and y will be -. A’’ is (-2, -5) Find points B and C using the same rule. B: (8,6) C: (4,9) B’: (-8, -6) C’: ( -4, -9)

No graph paper at home???? It’s OK! Rotate these around the ORIGIN!! A (3, -2) clockwise 90° B (0, 5) 180° C (-3,-7) counterclockwise 90° D (2,3) clockwise 90° E (-3, 6) 180° (3,-6) F (-7, -2) clockwise 90° G (5, 1) clockwise 270° (-,+) (+,+) (-,-) (+,-) (-2,-3) (0,-5) (7,-3) (3,-2) (-2,7) (-1,5)

The Transformation Song…. (tune of Happy and You Know It) When you REFLECT across the x, you change the y. (clap clap) When you REFLECT across the y, you change the x. (clap clap) When the numbers switch you’ll see, it’s across the origin you’ll be. Reflection is fun for you and me!

When you rotate 90 degrees, you switch the numbers. (stomp stomp) When you rotate ninety degrees, you check the quadrant. (stomp stomp) When you rotate 180 degrees, only the signs will switch you’ll see Rotation is fun for you and me!!

When you translate right or left, you move the x. (yippee) When you translate up or down, you move the y. (yippee) It’s the easiest one we’ve tried, all the figures do is slide Translation is fun for you and me.

ME