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QUESTION 7 In the diagram below, \( A(-1 ;-3), B \) and \( C \) are the vertices of a triangle. \( \mathrm{P}(2,5 ; 1) \) is the midpoint of \( \mathrm{AB} \). CA extended cuts the \( y \)-axis at \( \mathrm{D} \). The equation of \( \mathrm{CD} \) is \( y=-3 x+k \). \( \mathrm{CA} \mathrm{B}=\theta \). \( \alpha \) and \( \beta \) are the angles that \( A B \) and \( A C \) respectively make with the \( x \)-axis. 7.1 Determine the value of \( k \). (2) 7.2 Determine the coordinates of \( \mathrm{B} \). (2) 7.3 Determine the gradient of \( \mathrm{AB} \). 7.4 Calculate the size of 0 . 7.5 Calculate the length of AD. Leave your answer in surd form. 7.6 If \( \mathrm{AC}=2 \mathrm{AD} \) and \( \mathrm{AB}=\sqrt{113} \), calculate the length of \( C B \). [18] 9

          QUESTION 7
In the diagram below, \( A(-1 ;-3), B \) and \( C \) are the vertices of a triangle. \( \mathrm{P}(2,5 ; 1) \) is the midpoint of \( \mathrm{AB} \). CA extended cuts the \( y \)-axis at \( \mathrm{D} \).
The equation of \( \mathrm{CD} \) is \( y=-3 x+k \). \( \mathrm{CA} \mathrm{B}=\theta \).
\( \alpha \) and \( \beta \) are the angles that \( A B \) and \( A C \) respectively make with the \( x \)-axis.
7.1 Determine the value of \( k \).
(2)
7.2 Determine the coordinates of \( \mathrm{B} \).
(2)
7.3 Determine the gradient of \( \mathrm{AB} \).
7.4 Calculate the size of 0 .
7.5 Calculate the length of AD. Leave your answer in surd form.
7.6 If \( \mathrm{AC}=2 \mathrm{AD} \) and \( \mathrm{AB}=\sqrt{113} \), calculate the length of \( C B \).
[18]
9

QUESTION 7
In the diagram below, A(-1 ;-3), B and C are the vertices of a triangle. P(2,5 ; 1) is the midpoint of AB. CA extended cuts the y-axis at D.
The equation of CD is y=-3 x+k. CAB=θ.
α and β are the angles that A B and A C respectively make with the x-axis.
7.1 Determine the value of k.
(2)
7.2 Determine the coordinates of B.
(2)
7.3 Determine the gradient of AB.
7.4 Calculate the size of 0 .
7.5 Calculate the length of AD. Leave your answer in surd form.
7.6 If AC=2 AD and AB=√(113), calculate the length of C B.
[18]
9

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