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Class 10 students of KV MG railway colony (coordinates geometry) have been allotted a rectangular plot of land for gardening activitiy . saplings are planted on the boundary at a distance of 1 metre from each other there is a triangular grassy lawn in the plot as shown in the figure . the student has to sow seeds of flowering plants on the remaining area of the plot remaining area of the plot considered a as origin and are the questions given below 1 ) considering A as the origin what are the coordinates of A2 ) considering A as the origin what are the coordinates of P3 ) find find the coordinates of Q..4 ) considering sea as the origin find the coordinates of R5 ) the area of the triangle PQR is calculated using the two different co-ordinate systems once with A as origin and then with C as origin does the area of the triangle differ ? give reason for your answer |
| Answer» AKE 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 =21[x1(y2−y3)+x2(y3−y1)+X3(y1−y2)]First case-Area of △PQR=21[4(2−5)+3(5−6)+6(6−2)]=21(4×−3+3×−1+6×4)=21(−12−3+24)=29Sq.unitSecond case-Area of △PQR=21[12(6−3)+1 | |