5. Five marks example problems

1. If the points \(P(-1,-4)\), \(Q(b,c)\), and \(R(5,-1)\) are collinear and \(2b + c = 4\), then find the values of \(b\) and \(c\).

 

Answer:

 

The value of \(b =\)

 

The value of \(c =\)

 

2. The floor of a hall is covered with identitcal tiles which are in the shapes of triangles. One such triangle has the vertices \((-3,2)\), \((-1,-1)\) and \((1,2)\). If the floor of the hall is completely covered by \(110\) tiles, find the area of the floor.

 

 

Answer:

 

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

 

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

 

3. The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost \(₹ 1300\) per square feet. What will be the total cost for making the parking lot?

 

 

Answer:

 

Area of the parking lot \(=\)  \(sq. \ ft\).

 

Total cost for constructing the parking lot \(= ₹\)