Question

If A(-2,-1),B(a,0),C(4,b),D(1,2) are the vertex of the parallelogram, find the values of a and b​

Answer 1

Answer:

a = 1 , b = 3

Step-by-step explanation:

in a parallelogram the midpoints of the diagonals are equal

we use midpoint formula  = p(x,y) = x1 + x2/2 , y1 +y2/2

for line AC  :  -2+4/2 there fore x = 1

                       -1+b/2 there fore y = 1-b/2

for line BD :  take the above values as point of intersection or mid point and apply the same formula to derive the answer.

     

Answer 2

Step-by-step explanation:

A(-2,-1) B(a,0) C(4,b) D (1,2)

Let diagonals AC & BD intersect at a point O.

therefore; AO=OC & BO=OD [since, diagonals of a parallelogram bisect each other.]

then O is midpoint of AC

let O(x,y),

x= -2+4/2 = 1. [by midpoint theorem]

O is midpoint of BD

let O(x,y), y= 0+2/2 = 1. [by midpoint theorem]

therefore O(x,y) = (1,1)

since; O is midpoint of BD

therefore a+1/2 =1

1+a=2

a=1

similarly, O is midpoint of BD

b-1/2=1

b-1=2

b=3