Question

Prove that (-2,-1), (1. 0), (1, 3) and (-2, 3)
vertices of a parallelogram?

Answer 1

Answer:

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+4/2, -1+3/2)

⇒M(1,1)

(ii) Mid- point M' of diagonal QS

M ′(1+1/2, 0+2/2)

⇒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=  whole root of (a-c)^2 + (b-d)^2

PQ=RS

SP=QR

Hope it helps!