Question

If ABCD is a parallelogram whose vertices A(–2, 3), B(6, 7), C(8, 3), then D =

Answer 1

Answer:

D = ( 0 , -1 )

Step-by-step explanation:

Let the 4th vertex be D(a,b)

Midpoint of AC = Midpoint of BD

[(-2+8) / 2 , (3+3) /2] = [(6 +a) / 2 , (7+b) /2]

[By Midpoint formula: x,y = [( x1+x2) / 2 ,(y1 +y2)/2]

[ 6/2 , 6/2] = [(6 +a) / 2 , (7+b) /2]

6/2 = (6 +a) / 2 and 6/2 = (7+b) /2

6 = 6 +a and 6 = 7 + b

6 -6= a and 6 -7 = b

a = 0 and b = -1

Hence ,

the fourth vertex is D ( 0, -1).

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