Interactive graphing tool problem that asks the student to plot a circle.
Download file: GraphToolCircle.pg
DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'parserGraphTool.pl', 'PGcourse.pl');
Preamble
This example shows how to get student input in the form of a graph (a circle) by using interactive graphing tools. Load the parserGraphTool.pl macro for this.
$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 ]);
Setup
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 - $k)^2")->reduce;define the equation of the circle that is shown in the problem and solution.
The GraphTool method creates the graph tool object. The only argument is the correct answer. This is a string that contains a list of objects that the student will be expected to graph. Each object is a brace delimited list of the attributes of the object. The first attribute in each list is the type of object to be graphed, circle in this case. What the remaining attributes are depend on the type. For a circle the second attribute is whether the object is to be solid or dashed, the third attribute is the center of the circle, and the fourth attribute is a point on the circle.
The ->with method is then used to set options for the GraphTool object. In this case the options that are set are:
bBox: This is an array reference of four values xmin, ymax, xmax, ymin indicating the upper left and lower right corners of the visible graph.There is a default checker for the GraphTool that will mark correct a student answer that ‘looks’ like the correct one. This means that if a student adds two circles that are equivalent with one solid and one dashed, that if the solid one is plotted second, credit will be given. For simple graphs, the default should be sufficient. See Graph Tool, custom checker for an example of how to use a custom checker.
For more details, see the POD documentation
BEGIN_PGML
Graph the circle given by the following equation.
[`[$circle_eq_lhs] = [$r ** 2]`]
[_]{$gt}
END_PGML
Statement
This asks to graph the circle given by the equation. 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.
The solution is
[@ $gt->generateAnswerGraph @]*
END_PGML_SOLUTION
ENDDOCUMENT();
Solution
The solution describes how to obtain the graph of the circle from the equation.
The line [@ $gt->generateAnswerGraph @]* inserts the correct answer graph.