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