12 ABCD is a parallelogram. The coordinates of \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D are (-2, 3), (2, 4), (8, -3) and ( \(4 , - 4\) ) respectively.
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- Prove that AB and BD are perpendicular.
- Find the lengths of AB and BD and hence find the area of the parallelogram ABCD
- Find the equation of the line CD and show that it meets the \(y\)-axis at \(\mathrm { X } ( 0 , - 5 )\).
- Show that the lines BX and AD bisect each other.
- Explain why the area of the parallelogram ABCD is equal to the area of the triangle BXC.
Find the length of BX and hence calculate exactly the perpendicular distance of C from BX .