Standard +0.3 This is a multi-part coordinate geometry question requiring standard techniques: finding intersection points, calculating ratios using section formula, and computing triangle area. While it has 5 sub-parts, each involves routine methods (simultaneous equations, gradient comparison, area formula) with no novel insight required. The perpendicularity check and ratio calculation are slightly above basic recall, placing it just above average difficulty.
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 \(A C D\).
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 $A C D$.
\hfill \mbox{\textit{WJEC Unit 1 2018 Q2}}