Motion in the Coordinate Plane

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Presentation transcript:

Motion in the Coordinate Plane

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

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

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

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.

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)

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)

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)

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)

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

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

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)

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)

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)

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