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?
(i) Taking A as origin,
We will take AD as x-axis and AB as y-axis.
It can be observed that the coordinates of point P,Q, and R are (4, 6), (3, 2), and (6, 5) respectively
Area of the triangle PQR = 
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
= 
[4 (2 – 5) + 3 (5 – 6) + 6 (6 – 2)
= 
(-12 – 3 + 24)
= 
Square units
(ii) Taking C as origin, CB as x-axis, and CD as y-axis, the coordinates of vertices P, Q, and R are (12, 2), (13, 6),and (10, 3) respectively
Area of the triangle PQR = 
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 - y2)
= 
[12 (6 – 3) + 13 (3 – 2) + 10 (2 – 6)
= 
(36 + 13 – 40)
= 
Square units
It can be observed that the area of the triangle is same in both the cases