Edexcel C12 2018 October — Question 7

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2018
SessionOctober
TopicStraight Lines & Coordinate Geometry

7. The point \(A\) has coordinates \(( - 1,5 )\) and the point \(B\) has coordinates \(( 4,1 )\). The line \(l\) passes through the points \(A\) and \(B\).
  1. Find the gradient of \(l\).
  2. Find an equation for \(l\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers. The point \(M\) is the midpoint of \(A B\). The point \(C\) has coordinates \(( 5 , k )\) where \(k\) is a constant.
    Given that the distance from \(M\) to \(C\) is \(\sqrt { 13 }\)
  3. find the exact possible values of the constant \(k\).