QUESTION 5
In the diagram below, \( A, B \) and \( C \) are the vertices of a triangle. \( \mathrm{AC} \) is extended to cut the \( x \)-axis at D.
5.1 Calculate the gradient of:
5.1.1 AD
\( 5.1 .2 \quad \mathrm{BC} \)
5.2 Calculate the size of D?B.
(1)
(3)
5.3 Write down an equation of the straight line \( A D \).
5.4 Determine the coordinates of \( \mathrm{M} \), the midpoint of \( \mathrm{BC} \).
5.5 If \( \mathrm{G}(a ; b) \) is a point such that \( \mathrm{A}, \mathrm{G} \) and \( \mathrm{M} \) lie on the same straight line, show that \( b=2 a+1 \).
5.6 Hence calculate TWO possible values of \( b \) if \( \mathrm{GC}=\sqrt{17} \).
(6)
[20]
7
