The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare 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 Fig. 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 ΔPQR if C is the origin?Also calculate the areas of the triangles in these cases. What do you observe?

Question

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare 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 Fig. 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  ΔPQR if C is the origin?Also calculate the areas of the triangles in these cases. What do you observe?

Filo · Accepted Answer

(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 	riangle 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 	riangle PQR is P=(12,2),Q=(13,6)  ,R=(10,3) Area of the triangle =\dfrac{1}{2}\left[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)ight]First case-Area of 	riangle PQR=\dfrac{1}{2}\left[4(2-5)+3(5-6)+6(6-2)ight]= \dfrac{1}{2}\left(4	imes -3+3	imes -1+6	imes 4ight)= \dfrac{1}{2}\left(-12-3+24ight)=\dfrac{9}{2}Sq.unitSecond  case-Area of 	riangle PQR=\dfrac{1}{2}\left[12(6-3)+13(3-2)+10(2-6)ight]= \dfrac{1}{2}\left(12	imes 3+13	imes 1+10	imes- 4ight)= \dfrac{1}{2}\left(36+13-40ight)=\dfrac{9}{2}Sq.unitHence we observed that the area of the triangle in both case is equal.

Question Text	The Class $X$ students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare 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 Fig. 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 $Δ PQR$ if $C$ is the origin? Also calculate the areas of the triangles in these cases. What do you observe?
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