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The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the Figure. The students are to sow seeds of flowering plants 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 `Delta PQR` if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?

Text Solution

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(i) If we take A as origin then AD is X-axis and AB is the Y-axis Then the coordinates of the vertices of `△PQR` is `P=(4,6),Q=(3,2),R=(6,5)`
(ii) If we take C as origin then CB is X-axis and CD is the Y-axis Then the coordinates of the vertices of `△PQR` is `P=(12,2),Q=(13,6),R=(10,3)`
Area of the triangle = `1/2 [x_1(y_2 −y_3)+x_2(y_3−y_1 )+x_3 (y_1−y_2)]` ...
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