Question

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 A

2 ) considering A as the origin what are the coordinates of P

3 ) find find the coordinates of Q..

4 ) considering sea as the origin find the coordinates of R

5 ) 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 1

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 =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.unit

Second  case-

Area of △PQR=21[12(6−3)+1

Answer 2

Answer:

I hope it's helpful for you.