Kite with a side parallel to the x-axis
Kite with a side parallel to the x-axis
Secondary 3
12 marks
Original parallel to AM 360 Guided Practice (Geometry and Trigonometry)
The diagram shows a kite \(ABCD\) in which the side \(AB\) is parallel to the \(x\)-axis. The diagonals \(AC\) and \(BD\) intersect at \(T\).
- It is given that \(B\) is \((7,\ 2)\) and the equation of the diagonal \(AC\) is \(2y=x+7\).
- Find the coordinates of \(A\).[2]
- Find the equation of the diagonal \(BD\).[3]
- Hence find the coordinates of \(T\) and of \(D\).[4]
- Given also that the coordinates of \(C\) are \((11,\ 9)\), find the area of the kite \(ABCD\).[3]
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Answer:(i)(a) \(A=(-3,2)\) (b) \(y=-2x+16\) (c) \(T=(5,6)\), \(D=(3,10)\) (ii) \(70\text{ units}^2\)
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