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
Whilst writing this out perhaps i should be using where the equations of line AC and line BC are perpendicular.
gradient AC =
gradient BC =
maybe the second way is the quickest in the exam or are there shortcuts?
thanks earboth . maybe using pythagoras thm is just as quick as both come to the same quadratic.
i checked both pythagoras and gradient method and both resolve to (sorry mind was scrambled by the time i wrote above quadratic)
I checked the book and it gives the answer as 6, but
tells me that the answer is 1 or 5.