COMPUTER SCIENCE LESSONS

GRAPHIC PROGRAMS
LESSONS
Trapezoid Worksheet Algebra I
DILATIONS, TRANSLATIONS, REFLECTIONS


Answers to worksheet plotted in DrScheme
;; This uses the scaled cartesian plane code
;;--------------------> TRAPEZOID COMMANDS <------------------
;;1.  Original trapezoid
(line (make-posn -3 -1) (make-posn -1 -1) 'blue) ;;A to B
(line (make-posn -1 -1) (make-posn 1 -4) 'blue)  ;;B to D
(line (make-posn -4 -4) (make-posn 1 -4) 'blue) ;;C to D
(line (make-posn -4 -4) (make-posn -3 -1) 'blue) ;;C to A

;;2.  Dilation with scale factor of 1/2
(line (make-posn -3/2 -1/2) (make-posn -1/2 -1/2) 'red) ;;A to B
(line (make-posn -1/2 -1/2) (make-posn 1/2 -2) 'red)  ;;B to D
(line (make-posn -2 -2) (make-posn 1/2 -2) 'red) ;;C to D
(line (make-posn -2 -2) (make-posn -3/2 -1/2) 'red) ;;C to A

;;3.  Dilation with scale factor of 2
;;original trapezoid
(line (make-posn -6 -2) (make-posn -2 -2) 'green) ;;A to B
(line (make-posn -2 -2) (make-posn 2 -8) 'green)  ;;B to D
(line (make-posn -8 -8) (make-posn 2 -8) 'green) ;;C to D
(line (make-posn -8 -8) (make-posn -6 -2) 'green) ;;C to A

;;4.  Translation for new coordinate ( X+2 , Y-1 )
(line (make-posn -1 -2) (make-posn 1 -2) 'black) ;;A to B
(line (make-posn 1 -2) (make-posn 3 -5) 'black)  ;;B to D
(line (make-posn -2 -5) (make-posn 3 -5) 'black) ;;C to D
(line (make-posn -2 -5) (make-posn -1 -2) 'black) ;;C to A

;;5.  Reflection across Y-axis created with the coordinate (-X,Y) -> Use the opposite of "X"
(line (make-posn 3 -1) (make-posn 1 -1) 'blue) ;;A to B
(line (make-posn 1 -1) (make-posn -1 -4) 'blue)  ;;B to D
(line (make-posn 4 -4) (make-posn -1 -4) 'blue) ;;C to D
(line (make-posn 4 -4) (make-posn 3 -1) 'blue) ;;C to A

;;6.  Reflection across X-axis created with the coordinate (X,-Y) -> Use the opposite of "Y"
(line (make-posn -3 1) (make-posn -1 1) 'blue) ;;A to B
(line (make-posn -1 1) (make-posn 1 4) 'blue)  ;;B to D
(line (make-posn -4 4) (make-posn 1 4) 'blue) ;;C to D
(line (make-posn -4 4) (make-posn -3 1) 'blue) ;;C to A

;;7.  Horizontal Reflection on Quadrant I of a trapezoid
;;Original Trapezoid
(line (make-posn 6 3) (make-posn 7 6) 'green) ;;A to B
(line (make-posn 7 6) (make-posn 12 6) 'green)  ;;B to C
(line (make-posn 12 6) (make-posn 14 3) 'green) ;;C to D
(line (make-posn 14 3) (make-posn 6 3) 'green) ;;D to A
;;Horizontal Reflection
(line (make-posn 6 15) (make-posn 7 12) 'green) ;;A to B
(line (make-posn 7 12) (make-posn 12 12) 'green)  ;;B to C
(line (make-posn 12 12) (make-posn 14 15) 'green) ;;C to D
(line (make-posn 14 15) (make-posn 6 15) 'green) ;;D to A

;;8.  Vertical Reflection on Quadrant I of a trapezoid
;;Original Trapezoid
(line (make-posn 6 14) (make-posn 3 12) 'red) ;;A to B
(line (make-posn 3 12) (make-posn 3 7) 'red)  ;;B to C
(line (make-posn 3 7) (make-posn 6 6) 'red) ;;C to D
(line (make-posn 6 6) (make-posn 6 14) 'red) ;;D to A
;;Vertical Reflection
(line (make-posn 12 14) (make-posn 15 12) 'red) ;;A to B
(line (make-posn 15 12) (make-posn 15 7) 'red)  ;;B to C
(line (make-posn 15 7) (make-posn 12 6) 'red) ;;C to D
(line (make-posn 12 6) (make-posn 12 14) 'red) ;;D to A
TO REVIEW AND LEARN COPY SAMPLE CODE INTO SCHEME,
RUN, OBSERVE, COMPARE AND CONTRAST THE CODE!

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