Question

show that the points (-2,-3),(1,0),(4,3)and (1,2)taken in order are the vertices of a parallelogram​

Answer 1

Step-by-step explanation:

We have the points

P(−2,−1),Q(1,0),R(4,3) and S(1,2)

We know the property the of parallelogram that diagonals of parallelogram bisect each other.

Let us find out mid-point of line joining P and R and line joining Q and S

(i) Mid-point M of diagonal PR

M(

2

−2+4

,

2

−1+3

)

⇒M(1,1)

(ii) Mid-point M

′

of diagonal QS

M

′

(

2

1+1

,

2

0+2

)

⇒M

′

(1,1)

From (i) & (ii)

Mid-points M & M

′

are identical

⇒ Diagonals of the figure PQRS bisect each other and this property is enough to prove that it is a parallelogram.

Although we can also check by distance formula i.e. d=

(a−c)

2

+(b−d)

2

PQ=RS

SP=QR