Area using perpendicular distance

Calculate area of triangle using base and perpendicular height, where height is found using perpendicular distance from a point to a line

1 questions · Standard +0.8

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OCR C1 Q9
13 marks Standard +0.8
\includegraphics{figure_9} The diagram shows the parallelogram \(ABCD\). The points \(A\) and \(B\) have coordinates \((-1, 3)\) and \((3, 4)\) respectively and lie on the straight line \(l_1\).
  1. Find an equation for \(l_1\), giving your answer in the form \(ax + by + c = 0\), where \(a\), \(b\) and \(c\) are integers. [4]
The points \(C\) and \(D\) lie on the straight line \(l_2\) which has the equation \(x - 4y - 21 = 0\).
  1. Show that the distance between \(l_1\) and \(l_2\) is \(k\sqrt{17}\), where \(k\) is an integer to be found. [7]
  2. Find the area of parallelogram \(ABCD\). [2]