# Khan/khan-exercises

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 Midpoint of a segment
randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ]) POINTS[ 0 ] + POINTS[ 1 ] POINTS[ 1 ] + POINTS[ 2 ] POINTS[ 0 ] + POINTS[ 2 ]
randRange( 1, 9 ) randRangeNonZero( 2, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( 2, 9 ) COEF_1 * X + CONST_1 - COEF_2 * X ( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 )

POINTS[ 1 ] is the midpoint of \overline{SEG_TOTAL}

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( [ 5, 0 ], 0.10 ) ); graph.points.push( circle( [ 10, 0 ], 0.10 ) ); label( [ 0, 0 ], POINTS[ 0 ], "below" ); label( [ 5, 0 ], POINTS[ 1 ], "below" ); label( [ 10, 0 ], POINTS[ 2 ], "below" );

If:
\qquad SEG_1 = COEF_1x + CONST_1 and
\qquad SEG_2 = COEF_2x + CONST_2

Find SEG_TOTAL.

TOTAL

A midpoint divides a segment into two segments with equal lengths.

style({ stroke: BLUE, strokeWidth: 3 }); line( [ 0, 0 ], [ 5, 0 ] ); style({ stroke: GREEN, strokeWidth: 3 }); line( [ 5, 0 ], [ 10, 0 ] ); graph.points.toFront(); $( "#given1" ).css({ "color": BLUE });$( "#given2" ).css({ "color": GREEN });

\blue{SEG_1} = \green{SEG_2}

Substitute in the expressions that were given for each length:

\qquad \blue{COEF_1x + CONST_1} = \green{COEF_2x + CONST_2}

Solve for x:

\qquad expr([ "*", COEF_1 - COEF_2, "x" ]) = CONST_2 - CONST_1

Substitute X for x in the expressions that were given for SEG_1 and SEG_2:

\qquad SEG_1 = COEF_1(\pink{X}) + CONST_1 \qquad SEG_2 = COEF_2(\pink{X}) + CONST_2

\qquad SEG_1 = COEF_1 * X + CONST_1 \qquad SEG_2 = COEF_2 * X + CONST_2

\qquad SEG_1 = COEF_1 * X + CONST_1 \qquad SEG_2 = COEF_2 * X + CONST_2

To find the length SEG_TOTAL, add the lengths \blue{SEG_1} and \green{SEG_2}:

\qquad SEG_TOTAL = \blue{SEG_1} + \green{SEG_2}

\qquad SEG_TOTAL = \blue{COEF_1 * X + CONST_1} + \green{COEF_2 * X + CONST_2}