Ratio of segments on line

Find the ratio in which a point divides a line segment, or find coordinates given a ratio.

1 questions · Standard +0.3

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WJEC Unit 1 2018 June Q2
Standard +0.3
The points \(A\) and \(B\) have coordinates \(( - 1,10 )\) and \(( 5,1 )\) respectively. The straight line \(L\) has equation \(2 x - 3 y + 6 = 0\). a) The line \(L\) intersects the line \(A B\) at the point \(C\). Find the coordinates of \(C\).
b) Determine the ratio in which the line \(L\) divides the line \(A B\).
c) The line \(L\) crosses the \(x\)-axis at the point \(D\). Find the coordinates of \(D\).
d) i) Show that \(L\) is perpendicular to \(A B\).
ii) Calculate the area of the triangle \(A C D\).