GraphTool

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with many other problems:

• A graph tool with circle
• A graph tool with cubic
• A graph tool with line
• A graph tool with a number line
• A graph tool with custom checker
• A graph tool with points

Graph Tool

This example shows how to get student input in the form of a graph (a circle) by using interactive graphing tools.

Problem Techniques Index

PG problem file	Explanation
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGML.pl", "parserGraphTool.pl" ); TEXT(beginproblem());	Initialization: It is important to include the parseGraphTool.pl macro.
# Define the answer checker for the graph tool. # This checker allows the student to graph the correct circle multiple # times. The idea is that the graph is graded based on appearance. # No matter how many times the student graphs the correct circle, # the resulting graph appears the same. $gt_checker = sub { my ($correct, $student, $ans, $value) = @_; return 0 if $ans->{isPreview}; my $score = 0; my @errors; my $count = 1; # Get the center and point that define the correct circle and # compute the square of the radius. my ($cx, $cy) = $correct->[0]->extract(3)->value; my ($px, $py) = $correct->[0]->extract(4)->value; my $r_squared = ($cx - $px) ** 2 + ($cy - $py) ** 2; my $pointOnCircle = sub { my $point = shift; my ($x, $y) = $point->value; return ($x - $cx) ** 2 + ($y - $cy) ** 2 == $r_squared; }; # Iterate through the objects the student graphed and check to # see if each is the correct circle. for (@$student) { my $nth = Value::List->NameForNumber($count++); # This checks if the student input matches the circle, type # (solid or dashed), the center of the circle and # checks if a point is on the circle. $score += 1, next if ($_->extract(1) eq $correct->[0]->extract(1) && $_->extract(2) eq $correct->[0]->extract(2) && $_->extract(3) == $correct->[0]->extract(3) && $pointOnCircle->($_->extract(4))); # The following gives additional information to the student. push(@errors, "The $nth object graphed is not a circle"), next if ($_->extract(1) ne $correct->[0]->extract(1)); push(@errors, "The $nth object graphed should be a " . $correct->[0]->extract(2) . " circle."), next if ($_->extract(2) ne $correct->[0]->extract(2)); push(@errors, "The $nth object graphed is incorrect."); } return ($score, @errors); }; $h = non_zero_random(-5, 5); $k = non_zero_random(-5, 5); $r = random(1, 4); Context()->variables->add("y" => "Real"); $circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce; $gt = GraphTool("{circle, solid, ($h, $k), ($h + $r, $k)}")->with( bBox => [-11, 11, 11, -11], cmpOptions => { list_checker => $gt_checker } );	Setup: The subroutine $gt_checker at the top is the answer checker. It checks if the student input matches the correct answer. The variables $h, $k and $r randomly pick a center and radius of the circle. The lines: Context()->variables->add("y" => "Real"); $circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce; are used to print out nicely the equation of the circle. The command GraphTool creates the graph tool (the axes and input buttons for the various types of graphs). The first argument is a string surrounded by {}. The arguments are: The type of geometric figure (circle, line, parabola or fill) The type of figure (solid or dashed) Other information about the figure. For example, with the circle, the center and another point on the circle. See Graph Objects for more details. Other parameters of the GraphTool can be set using with. The following include other features: bbox: this is an array reference of four values xmin, ymax, xmax, ymin indicating the upper left and lower right corners of the visible graph. cmpOptions: this is a hash of options passed to the cmp method for checking the answer. The example here: cmpOptions => { list_checker => $gt_checker } has the checker use the one we defined above. More documentation can be found at: [1]
BEGIN_PGML Graph the circle given by the following equation. [`[$circle_eq_lhs] = [$r ** 2]`] [_]{$gt} END_PGML	Main Text: This asks to graph the circle given by the equation. And the code: [_]{$gt} inserts the GraphTool.
BEGIN_PGML_SOLUTION The equation of the circle of the form: [`[$circle_eq_lhs] = [$r ** 2]`] has a center at [`([$h],[$k])`] and radius [$r]. To enter the graph, click the circle tool, then click the center at [`([$h],[$k])`] and then click a second point that is [$r] units from the center. This is easist going left, right, up or down from the center. END_PGML_SOLUTION ENDDOCUMENT();	This is the solution.

Problem Techniques Index

• POD documentation: [2]