1.   Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

2.   Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).

3.   To conduct Sports Day activities, in your  rectangular  shaped  school ground  ABCD,  lines  have 
	 been drawn  with  chalk  powder  at  a distance of 1m each. 100 flower pots have been placed at a distance
	 of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs $1/4$th the distance  AD  on  the  
	 2nd  line  and posts a green flag. Preet runs $1/5$th the distance AD on the eighth line and  posts  a
	 red  flag.  What  is  the distance between both the flags? If Rashmi has to post a blue flag exactly 
	 halfway  between  the  line  segment joining the two flags, where should she post her flag?

 4.   Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
 
 5.   Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis.
      Also find the coordinates of the point of division.
	  
6.   If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

7.   Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

8.   If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = $3/7$ AB and 
      P lies on the line segment AB.
	  
9.   Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

10.   Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. 

Solution