1. Motion in the Coordinate Plane

2. Label the following on the graph.y
x-axis
y-axis
origin
Quadrants I, II, III, IV II I
origin x
III IV

3. Cartesian Coordinates
(x, y)
tells how far left or right to go from the origin
tells how far up or down to go from the origin

4. Graph the following points and label with the appropriate letter.
C(-4,-1)
D(-3,1)
E(0,5)
F(-2,0)
G(5,-2) E A D B F C G

5. Transformations on the Coordinate Plane
Identify the coordinates of each vertex.
Plug the coordinates into the rule.
Plot the new points and connect.
Identify the transformation.

6. translated figure up 3 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x, y+3)
Add 3 to the y’s.
Preimage
Image
(1,3)
(1, 6)
(1,1)
(1, 4)
translated figure up 3 units
(4,1)
(4, 4)

7. translated figure right 5 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x+5, y)
Add 5 to the x’s.
Preimage
Image
(-4,3)
(1, 3)
(-4,1)
(1, 1)
translated figure right 5 units
(-1,1)
(4, 1)

8. translated figure left 2 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x-2, y)
Subtract 2 from x’s
Preimage
Image
(-3,-2)
(-5, -2)
(-3,-4)
(-5, -4)
translated figure left 2 units
(0,-4)
(-2, -4)

9. translated figure down 4 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x, y–4)
Subtract 4 from y’s.
Preimage
Image
(2,1)
(2, -3)
(2,-1)
(2, -5)
translated figure down 4 units
(5,-1)
(5, -5)

10. Summary of Translations
Add to x
Translates RIGHT
Subtract from x
Translates LEFT
Add to y
Translates UP
Subtract from y
Translates DOWN

11. Describe each transformation.
(x+10, y)
(x–5, y)
(x, y+7)
(x, y–6)
(x+3,y–7)
(x–4,y–5)
(x–8,y+9)
translates right 10
translates left 5
translates up 7
translates down 6
translates right 3
and down 7
translates left 4
and down 5
translates left 8
and up 9

12. Reflects the figure over the y-axis
Use the given rule to transform the figure. Then describe the transformation.
Rule: (-x, y)
0pposite of x’s
Preimage
Image
(1,3)
(-1,3)
(1,1)
(-1,1)
Reflects the figure over the y-axis
(4,1)
(-4,1)

13. Reflects the figure over the x-axis
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x, -y)
0pposite of y’s
Preimage
Image
(1,5)
(1,-5)
(1,3)
(1,-3)
Reflects the figure over the x-axis
(4,3)
(4,-3)

14. Use the given rule to transform the figure
Use the given rule to transform the figure. Then describe the transformation.
Rule: (-x, -y)
opposite of x’s
opposite of y’s
Preimage
Image
(4,5)
(-4,-5)
(2,1)
(-2,-1)
Rotates the figure 180°
(4,1)
(-4,-1)

15. Summary of Reflections and Rotations
(-x,y)
Reflects over y-axis
(x,-y)
Reflects over x-axis
(-x,-y)
Rotates figure 180°