Question

(a) Taking A as origin, find the coordinates of the vertices of the triangle,
(i) P (4, 6), Q(3, 2), R(6,5)
(ii) P (3, 2), Q(4,6), R(6,5)
(iii) P (4,6), Q(3, 2), R(5, 6)
(iv) P (4, 6), Q(2,3), R(6,5)​

Answer 1

Answer: 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 △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 =  

2

1

​

[x  

1

​

(y  

2

​

−y  

3

​

)+x  

2

​

(y  

3

​

−y  

1

​

)+x  

3

​

(y  

1

​

−y  

2

​

)]

First case-

Area of △PQR=  

2

1

​

[4(2−5)+3(5−6)+6(6−2)]

=  

2

1

​

(4×−3+3×−1+6×4)

=  

2

1

​

(−12−3+24)=  

2

9

​

Sq.unit

Second  case-

Area of △PQR=  

2

1

​

[12(6−3)+13(3−2)+10(2−6)]

=  

2

1

​

(12×3+13×1+10×−4)

=  

2

1

​

(36+13−40)=  

2

9

​

Sq.unit

Hence we observed that the area of the triangle in both case is equal.

Step-by-step explanation:

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