The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Distance, midpoint and geometric reasoning
Calculate exact distances and full midpoint coordinates.
Recover missing endpoints and all permitted points.
Use squared lengths and midpoint properties to justify geometric claims.
For \(A(x_1,y_1)\), \(B(x_2,y_2)\): \(AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\), \(\displaystyle M= \bigl (\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2}\bigr )\). Equal distances alone do not make a point a midpoint: it must also lie on the segment.