2. Two marks example problem

1. Find the area of the triangle whose vertices are \((-3,5)\), \((5,6)\) and \((5,-2)\).

 

Answer:

 

The area of the triangle \(=\)  \(sq. \ units\).

 

2. Show that the points \(P(-1.5,3)\), \(Q(6,-2)\), \(R(-3,4)\) are collinear.

 

Answer:

 

Area of the triangle \(=\)  \(sq. \ units\).

 

Therefore, the points \(P(-1.5,3)\), \(Q(6,-2)\), \(R(-3,4)\) are collinearnot collinear.

 

3. If the area of the triangle formed by the vertices \(A(-1,2)\), \(B(k,-2)\) and \(C(7,4)\) (taken in order) is \(22 \ sq. \ units\), find the value of \(k\).

 

Answer:

 

The value of \(k =\) .

 

4. Find the area of the quadrilateral formed by the points \((8,6)\), \((5,11)\), \((-5,12)\) and \((-4,3)\).