randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ])
POINTS[ 0 ] + POINTS[ 1 ]
POINTS[ 1 ] + POINTS[ 2 ]
POINTS[ 0 ] + POINTS[ 2 ]
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRange( 1, 9 )
( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 )
shuffle([
[ BLUE, SEG_1 + " = " + COEF_1 + "x + " + CONST_1 ],
[ GREEN, SEG_2 + " = " + COEF_2 + "x + " + CONST_2 ],
[ "purple", SEG_TOTAL + " = " + TOTAL ]
])
If:
\qquad GIVEN[ 0 ][ 1 ],
\qquad GIVEN[ 1 ][ 1 ], and
\qquad GIVEN[ 2 ][ 1 ],
Find SEG_2.
init({
range: [ [ -1, 11 ], [ -1, 1 ] ]
});
line( [ 0, 0 ], [ 10, 0 ] );
style({ stroke: "#000", fill: "#000" });
graph.points = raphael.set();
graph.points.push( circle( [ 0, 0 ], 0.10 ) );
graph.points.push( circle( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], 0.10 ) );
graph.points.push( circle( [ 10, 0 ], 0.10 ) );
label( [ 0, 0 ], POINTS[ 0 ], "below" );
label( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], POINTS[ 1 ], "below" );
label( [ 10, 0 ], POINTS[ 2 ], "below" );
COEF_2 * X + CONST_2
style({ stroke: BLUE, strokeWidth: 3 });
line( [ 0, 0 ], [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ] );
style({ stroke: GREEN, strokeWidth: 3 });
line( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], [ 10, 0 ] );
graph.points.toFront();
$( "#given0" ).css({ "color": GIVEN[ 0 ][ 0 ] });
$( "#given1" ).css({ "color": GIVEN[ 1 ][ 0 ] });
$( "#given2" ).css({ "color": GIVEN[ 2 ][ 0 ] });
From the diagram, we can see that the total length of \purple{SEG_TOTAL} is the sum of \blue{SEG_1} and \green{SEG_2}:
\qquad \blue{SEG_1} + \green{SEG_2} = \purple{SEG_TOTAL}
Substitute in the expressions that were given for each length:
\qquad \blue{COEF_1x + CONST_1} + \green{COEF_2x + CONST_2} = \purple{TOTAL}
Combine like terms:
\qquadCOEF_1 + COEF_2x + CONST_1 + CONST_2 = \purple{TOTAL}
Subtract CONST_1 + CONST_2 from both sides:
\qquadCOEF_1 + COEF_2x = TOTAL - CONST_1 - CONST_2
Divide both sides by COEF_1 + COEF_2 to find x:
\qquad x = X
Substitute X for x in the expression that was given for SEG_2:
\qquad SEG_2 = COEF_2(\pink{X}) + CONST_2
Simplify:
\qquad \green{SEG_2 = COEF_2 * X + CONST_2}
Simplify to find \green{SEG_2}:
\qquad \green{SEG_2 = COEF_2 * X + CONST_2}