10 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.