** Using WeBWorK **

Thanks in advance for your suggestions, Tom

## DESCRIPTION ## KEYWORDS('vectors', 'independent', 'dependent', 'relation') ## ## ENDDESCRIPTION

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros( PG.pl, PGbasicmacros.pl, PGchoicemacros.pl, PGanswermacros.pl, PGgraphmacros.pl, PGmatrixmacros.pl, PGnumericalmacros.pl, PGauxiliaryFunctions.pl, PGmorematrixmacros.pl, PGdiffeqmacros.pl, "Parser.pl", "Generic.pl" );

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

$p1 = non_zero_random(-6,6,1); $p2 = random(-5,5,2); $q1 = non_zero_random(-6,6,1); $q2 = random(-6,6,2);

$ans1 = $q1-$p1; $ans2 = $q2-$p2; $vecp = Matrix->new_column_matrix([$p1, $p2]); $slope = Matrix->new_column_matrix([$ans1, $ans2]);

$v1 = new Matrix(2,1); $v1->assign(1,1, $ans1); $v1->assign(2,1, $ans2);

BEGIN_TEXT

Enter a point on the line { mbox( '( v = )', display_matrix($vecp), '( + t) ', display_matrix($slope), '.' ) } $BR { mbox( '(x=)', answer_matrix(2,1,5) ) }

END_TEXT

$spot=0; ANS(generic_cmp("1", type => 'Number', length=>1, checker=> ~~&check)); ANS(generic_cmp("1", type => 'Number', length=>1, checker=> ~~&check));

sub check{</p><p> my $stu=shift();</p><p> $w[$spot]=$stu->extract(1); </p><p> if($spot<1){</p><p> $spot=$spot+1; 1; </p><p> }else{</p><p> $ww[0]=$w[0]-$p1;</p><p> $ww[1]=$w[1]-$p2;</p><p> $avec1=$v1->element(1,1);</p><p> $avec2=$v1->element(2,1);</p><p> if($avec1 * $ww[1] == $ww[0] * $avec2){</p><p> 1;</p><p> }else{</p><p> 0;</p><p> } } }

ENDDOCUMENT() ;

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     if ($avec1 * $ww[1] == $ww[0] * $avec2) ...

Since you have loaded Parser.pl, you could use the the fuzzy checks that are built into the Real number objects:

    if (Real($avec1 * $ww[1]) == Real($ww[0] * $avec2)) ...

Another problem is that you are always marking the x-coordinate as correct, so the student will always get partial credit for the problem. This is a bit awkward. It also could fail in the case where you have a vertical line (which is possible given your range of random numbers), since the student could enter an x-value that is off the line, but it will still be marked correct.

On a more general note, you are working a lot harder than you need to in this problem. Here is an alternative approach that uses the Parser to better effect.

    DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGanswermacros.pl",
"Parser.pl",
"parserVectorUtils.pl",
);

TEXT(beginproblem());

Context("Vector")->variables->are(t=>'Real');
$t = Formula("t");

$p = non_zero_vector2D(-6,6,1)->with(ColumnVector=>1);
$v = non_zero_vector2D(-5,5,1)->with(ColumnVector=>1);

$L = $p + $t*$v;

Context()->texStrings;
BEGIN_TEXT

Enter a point on the line \($L\).
$PAR
\(x=\)\{$p->ans_array\}

END_TEXT
Context()->normalStrings;

ANS($p->cmp(showCoordinateHints=>0, checker=> sub {<br /> my $correct = shift; my $student = shift;<br /> return $student == $p || $v->isParallel($student-$p);<br /> }));

$showPartialCorrectAnswers = 0;

ENDDOCUMENT();

Here, we use the parser's Vector objects to produce some column vectors for the point and vector for the line, and then combine them into the formula for a line. Because of the Context()->texStrings, the $L in the text area will produce its TeX form automatically. Then the x value is requested using an answer array. Finally, the answer checker automatically collects the entries for the array into a vector, and the checker subroutine checks if the student's point is the same as the one used to generate the line, or if the vector from the starting point to the student's answer is to the line's vector.

Hope this helps.

Davide

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Davide

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I'm not developing it any further, and have already converted all the problems I wrote with it. Conversion is usually pretty routine. Thanks for trying it out!

Bob

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Davide

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