The midpoint is M((x_1+x_2)/2,(y_1+y_2)/2). It is halfway through both the horizontal and vertical changes. Average each coordinate separately. If M and A are known, solve B=2M-A coordinate by coordinate. Check that the two endpoint changes from M are opposites. If A=(-2,5), M=(1,3), then B=(2(1)-(-2),2(3)-5)=(4,1). Check: subtracting the two endpoints and dividing by two gives a displacement, not the midpoint position.

The midpoint is \(M((x_1+x_2)/2,(y_1+y_2)/2)\). It is halfway through both the horizontal and vertical changes.

Average each coordinate separately. If \(M\) and \(A\) are known, solve \(B=2M-A\) coordinate by coordinate. Check that the two endpoint changes from \(M\) are opposites.

If \(A=(-2,5)\), \(M=(1,3)\), then \(B=(2(1)-(-2),2(3)-5)=(4,1)\).

Check: subtracting the two endpoints and dividing by two gives a displacement, not the midpoint position.

Midpoints and missing endpoints

Midpoints and missing endpoints