Advanced coordinate geometry: Using Coordinate Geometry to Find Missing Points

Advanced coordinate geometry: Using Coordinate Geometry to Find Missing Points

Solutions to this question by accurate drawing will not be accepted.
\(A\), \(B\) and \(C\) are the points \(\left( -10,15 \right)\), \(\left( -10,-10 \right)\) and \(\left( 10,-20 \right)\).

  1. Find the area of triangle \(ABC\).
  2. \(ABCD\) is a parallelogram. Find the coordinates of the point \(D\).
  3. \(ABCE\) is a trapezium with \(AB\) parallel to \(CE\). The area of the trapezium is \(650\) units\(^{2}\).
    Find the coordinates of the point \(E\).

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Answer:(a) \(250\text{ units}^2\) (b) \(D=(10,5)\) (c) \(E=(10,20)\)

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