Question 2 - A-Level Maths

Exam Board	AQA
Module	C1 (Core Mathematics 1)
Year	2006
Session	January
Topic	Straight Lines & Coordinate Geometry

2 The point \(A\) has coordinates \(( 1,1 )\) and the point \(B\) has coordinates \(( 5 , k )\). The line \(A B\) has equation \(3 x + 4 y = 7\).

1. Show that \(k = - 2\).
2. Hence find the coordinates of the mid-point of \(A B\).
Find the gradient of \(A B\).
The line \(A C\) is perpendicular to the line \(A B\).
1. Find the gradient of \(A C\).
2. Hence find an equation of the line \(A C\).
3. Given that the point \(C\) lies on the \(x\)-axis, find its \(x\)-coordinate.