Hi all,

The points A(-1,-2), B(7,2) and C(k,4), where K is a constant, are the vertices of

ABC. Angle ABC is a right angle.

a) Find the gradient of AB

b) Calculate the value of K.

c) Show that the length of AB may be written in the form

, where p is an integer to be found.

d) Find the exact value of the area

ABC.

e) Find an equation for the straight line l passing through B and C. Give your answer in the form ax + by +c = 0, where a,b, and c are integers.

Can someone please indicate the easiest (less time consuming way of answering part b)

I worked out the equations for AC and BC using

so

and

so solve

Whilst writing this out perhaps i should be using

where the equations of line AC and line BC are perpendicular.

so

gradient AC =

gradient BC =

then

then solve

maybe the second way is the quickest in the exam or are there shortcuts?

thanks sammy