AQA C1 2005 June — Question 1

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2005
SessionJune
TopicStraight Lines & Coordinate Geometry

1 The point \(A\) has coordinates \(( 6,5 )\) and the point \(B\) has coordinates \(( 2 , - 1 )\).
  1. Find the coordinates of the midpoint of \(A B\).
  2. Show that \(A B\) has length \(k \sqrt { 13 }\), where \(k\) is an integer.
    1. Find the gradient of the line \(A B\).
    2. Hence, or otherwise, show that the line \(A B\) has equation \(3 x - 2 y = 8\).
  3. The line \(A B\) intersects the line with equation \(2 x + y = 10\) at the point \(C\). Find the coordinates of \(C\).