Midpoints and geometric measurements

The midpoint of \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\). Average the two x-coordinates and the two y-coordinates separately.

If the midpoint \(M\) and one endpoint \(A\) are known, the other endpoint is \((2x_M-x_A,\ 2y_M-y_A)\). Check that your midpoint lies halfway between the endpoints.

For a triangle, \(\text{area}=\dfrac12\times\text{base}\times\text{perpendicular height}\). With a horizontal base, the height is the vertical difference; it is not the length of a sloping side.

Midpoint and area calculations use coordinates as measurements. Use a diagram to identify the relevant distances before calculating.