1 Point A has coordinates ( 4,7 ) and point B has coordinates ( 2,1 ).
- Find the equation of the line through A and B .
- Point C has coordinates \(( - 1,2 )\). Show that angle \(\mathrm { ABC } = 90 ^ { \circ }\) and calculate the area of triangle ABC .
- Find the coordinates of \(D\), the midpoint of AC.
Explain also how you can tell, without having to work it out, that \(\mathrm { A } , \mathrm { B }\) and C are all the same distance from D.