ExtractingCoordinatesFromPoint

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Extracting coordinates from a Point: PG Code Snippet

This code snippet shows the essential PG code to evaluate antderivative and general antiderivative formulas. Note that these are insertions, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.

This wiki page is under construction as of 6/13/08.

Problem Techniques Index

PG problem file	Explanation
loadMacros("MathObjects.pl");	In the initialization section, we need to include the macros file MathObjects.pl.
Context( "Point" ); push(@point, Point(random(1,5,1), random(-5,-1,1))); push(@point, Point(random(5,10,1), random(6,11,1))); # now we have two points, $point[0] = (x1,y1) # and $point[1] = (x2,y2). # the following makes $d1 = x1 - x2, $d2 = y1 - y2 ($d1, $d2) = ($point[0] - $point[1])->value; $length = Compute("sqrt( ($d1)^2+($d2)^2 )"); $mid = ( $point[1] + $point[0] ) / 2;	In the problem setup section of the file, we put the value of the subtraction of two Points in two variables, $d1, the x coordinate, and $d2, the y coordinate. This is achieved by calling Point's value method, as shown. Alternative method: If you want to get only one of the coordinates of a Point, you can use the extract method, for example: $x = $point->extract(1);. This gets the first coordinate of $point (x) and assigns it to the variable $x. We don't use Context("Vector"); and norm( $point[0] - $point[1] ) here to determine length because we don't want to accept an answer like |<5,7>-<7,8>|. Alternative method: You can use $length=norm( $point[0] - $point[1] ); with Context("Vector"); if you want to accept answers that are valid in the Vector context (such as the absolute value of a vector). We need to put parentheses around $d1 and $d2 in the Compute expression because if $d1 = -6, then -6^2 = -36, not 36, as desired. However, if the code is ($d1)^2 then that evaluates as (-6)^2 = 36, as desired.
Context()->texStrings; BEGIN_TEXT Consider the two points \( $point[0] \) and \( $point[1] \). The distance between them is: \{ $length->ans_rule() \} $BR The midpoint of the line segment that joins them is:\{ $mid->ans_rule() \} $BR END_TEXT Context()->normalStrings;	The problem text section of the file is as we'd expect.
ANS( $length->cmp ); ANS( $mid->cmp );	As is the answer.

Problem Techniques Index