randRange( -8, 7 ) randRange( -7, 8 ) randRange( -9, 8 ) randRange( -9, 8 ) ( X1 + X2 ) / 2 ( Y1 + Y2 ) / 2

What is the midpoint of the line segment from (X1, Y1) to (X2, Y2)?

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->", }); path([ [ X1, Y1 ], [ X2, Y2 ] ], {stroke:"#000000"}); style( point1Style ); label( [ X1, Y1 ], "(" + X1 + ", " + Y1 + ")", getPos( [ X1,Y1 ], [ X2, Y2 ]) ); circle( [ X1, Y1 ], 0.15 ); style( point2Style ); label( [ X2, Y2 ], "(" + X2 + ", " + Y2 + ")", getPos( [ X2,Y2 ], [ X1, Y1 ]) ); circle( [ X2, Y2 ], 0.15 );
\Large{(}XM, YM\Large{)}

integers, like 6

simplified proper fractions, like 3/5

simplified improper fractions, like 7/4

a mixed number, like 1\ 3/4

and/or exact decimals, like 0.75

The x coordinate of the midpoint is the average of the x coordinates X1 and X2.

x = \dfrac{1}{2}(X1 + X2)

x = \dfrac{1}{2}(X1 + X2)

x = XM

style( midPtStyle ); graph.vert = path( [ [ XM, -10], [ XM, 10] ] );

The y coordinate of the midpoint is the average of the y coordinates Y1 and Y2.

y = \dfrac{1}{2}(Y1 + Y2)

y = \dfrac{1}{2}(Y1 + Y2)

y = YM

graph.horiz = path( [ [ -10, YM], [ 10, YM ] ] );

The midpoint is (XM, YM).

circle( [ XM, YM ], 0.15 ); label( [ XM, YM ], "(" + XM + ", " + YM + ")", getPos( [ XM, YM ], [ X1, Y1 ]) );
graph.vert.remove(); graph.horiz.remove();

The point (XM, YM) is the midpoint of (X1, Y1) and what point?

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->", }); style( point1Style ); label( [ X1, Y1 ], "(" + X1 + ", " + Y1 + ")", getPos( [ X1,Y1 ], [ XM, YM ]) ); graph.first = circle( [ X1, Y1 ], 0.15 ); style( midPtStyle ); label( [ XM, YM ], "(" + XM + ", " + YM + ")", getPos( [ XM, YM ], [ X1, Y1 ]) ); graph.midpoint = circle( [ XM, YM ], 0.15 );
(X2, Y2)

integers, like 6

simplified proper fractions, like 3/5

simplified improper fractions, like 7/4

a mixed number, like 1\ 3/4

and/or exact decimals, like 0.75

The average of the desired x coordinate and X1 should be XM.

\dfrac{1}{2}(x + X1) = XM

Solving for x:

x + X1 = (2 * XM)

x = X2

style( point2Style ); graph.vert = path( [ [ X2, -10], [ X2, 10] ] );

The average of the desired y coordinate and Y1 should be YM.

\dfrac{1}{2}(y + Y1) = YM

Solving for y:

y + Y1 = (2 * YM)

y = Y2

graph.horiz = path( [ [ -10, Y2 ], [ 10, Y2 ] ] );

The point (XM, YM) is the midpoint of (X1, Y1) and (X2, Y2). path([ [ X1, Y1 ], [ X2, Y2 ] ], {stroke:"#000000"}); circle( [ X2, Y2 ], 0.15 ); label( [ X2, Y2 ], "(" + X2 + ", " + Y2 + ")", getPos( [ X2, Y2 ], [ XM, YM ]) ); graph.first.toFront(); graph.midpoint.toFront();

graph.vert.remove(); graph.horiz.remove();