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 th thedistance AD on the 2nd line andposts a green flag. Preet runsththe distance AD on the eighth lineand posts a red flag. What is thedistance between both the flags? IfRashmi has to post a blue flag exactlyhalfway between the line segmentjoining the two flags, where shouldshe post her flag?
The Class X students of asecondary school inKrishinagarhave been allotteda rectangular plot of land fortheir gardening activity.Sapling of Gulmohar areplanted on the boundary at adistance of 1m from each other.There is a triangular grassylawn in the plot as shown inthe Fig. 7.14. The students areto sow seeds of floweringplants on the remaining area of the plot
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
Let A (4, 2), B(6, 5) and C (1, 4) be the vertices of Δ ABC
(i) The median from A meets BC at D. Find the coordinates of the point D
(ii) Find the coordinates of the point P on AD such that AP: PD = 2: 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1
(iv) What do you observe?
[Note: The point which is common to all the three medians is called the centroidand this point divides each median in the ratio 2: 1]
(v) If and are the vertices of Δ ABC, find the coordinates of the centroid of the triangle