Q.1. Find the coordinates of the point which divides the join of (–1,7) and (4, –3) in the ratio 2:3.; Q.2. Find the coordinates of the points of trisection of the line segment joining (4,–1) and (–2,–3).; Q.3 To conduct sport day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flowers pots have been placed at a distance of 1m from each other along AD as shown in the figure. 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 8th line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly half way between the line segment joining the two flags, where should she post her flag?; Q.4. Find the ratio in which the line segment joining points (-3,10) and (6,-8) is divided by (-1,6).; Q.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 point of division.; Q.6. If (1,2), (4,y), (x,6) and (3,5) are the vertices of a parallelogram taken in order, find x and y.; Q.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).; Q.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.; Q.9. Find the coordinates of the points which divide the line segment joining A(-2,2) and B(2,8) into four equal parts.; Q.10. Find the area of a rhombus if its vertices are (3,0), (4,5), (-1,4) and (-2, -1) taken in order. [Hint: Area of a rhombus = (1/2) ×(product of its diagonals)]
