nIf A(6,1), B(8,2), C(9,4), & D(7,3) are the vertices of ABCD, show that ABCD is a parallelogram . -: ANSWER :-Given : -If A(6,1), B(8,2), C(9,4), & D(7,3) are the vertices of ABCD, show that ABCD is a parallelogram .Required to find : - ABCD is a parallelogram Formula used : - Distance between 2 POINTS = √[(x1-x)²+(y1-y)²]Solution : - Here,We need to show that ABCD is a parallelogramWe already know that;In a parallelogram, opposite sides are equal So,AB = CD BC = AD Using this CONCEPT let's solve this question ! The formula which we are going to USE is;Distance between 2 points = √[(x1-x)²+(y1-y)²]Here,x1 & x can be any co-ordinate The co-ordinates of the parallelogram are; A(6,1) B(8,2)C(9,4)D(7,3)Distance between the points A&B = √[(8-6)²+(2-1)²]AB = √[(2)²+(1)²]AB = √[4+1]AB = √5 unitsNow,Let's find the distance between B&C = √[(9-8)²+(4-2)²]BC = √[(1)²+(2)²]BC = √[1+4]BC = √5 units Now,Let's find the distance between C&D = √[(7-9)²+(3-4)²]CD = √[(-2)²+(-1)²]CD = √[4+1]CD = √5 units Let's find the distance between A & D = √[(7-6)²+(3-1)²]AD = √[(1)²+(2)²]AD = √[1+4]AD = √5 units HENCE,AB = √5 units BC = √5 units CD = √5 units AD = √5 units From the above we can conclude that; ABCD is not a parallelogram, but actually it is a square In a square, All sides are equal . However,The square is defined as;It is a parallelogram which has all it's sides equal . Therefore,ABCD is not a parallelogram ✓