2026 YTSS P2 Q4

Solutions to this question by accurate drawing will not be accepted.

The diagram below shows 4 points, \(A,B,C\) and \(D\).

Points \(B\) and \(D\) lie on the \(x\)-axis and point \(C\) lies on the \(y\)-axis.

\(B\) is the point \((2,0)\) and \(AB\) intersects the \(y\)-axis at 1.

It is given further that \(BC\) is parallel to \(AD\) and the equation of the line \(AD\) is \(y-4-x=0\).

1. Find the equation of the line \(AB\).[2]
2. Show that the coordinates of \(A\) are \((-2,2)\).[2]
3. 1. Find distance \(AC\).[2]
   2. Find the shortest distance from \(B\) to \(AC\) given that the area of \(ABC\) is 6 units\(^2\).[2]