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Coordinate Geometry and Vector Applications

Coordinate Geometry and Vector Applications

TGM Original

The points \(A\), \(B\) and \(C\) are vertices of a triangle. The point \(A\) is \((-1,3)\) and the gradient of the line \(AB\) is \(2\).

  1. Find the equation of the line \(AB\).
  2. The equation of the line \(BC\) is \(2x+y=17\). Find the coordinates of \(B\).
  3. It is given that \(\overrightarrow{AE} = \begin{pmatrix} 4 \\ 12 \end{pmatrix}\). Find the coordinates of \(E\).
  4. Given also that \(D\) is \((3,7)\), express as a column vector:
    1. \(\overrightarrow{DE}\).
    2. \(\overrightarrow{DB}\).
  5. What two facts can be deduced about \(D\), \(E\) and \(B\).

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Answer:(a) \(y=2x+5\) (b) \(B=(3,11)\) (c) \(E=(3,15)\) (d)(i) \(\begin{pmatrix}0\\8\end{pmatrix}\) (ii) \(\begin{pmatrix}0\\4\end{pmatrix}\) (e) \(D,B,E\) are collinear and \(B\) is the midpoint of \(DE\).

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