Question

Given two adjacent vertices of a parallelogram A (3,5), B (1,7) and the point of intersection of their diagonals M (1,1), determine the coordinates of the other two
vertices.

Answer 1

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Answer:

A (3,5), B (1,7) ,C(-1,-3),D(1,-5)

Explanation:

M[1,1]=                                  [Diagonals bisect each other]

$[ \frac{x_{1} + x_{2}}{2} , \frac{y_{1} + y_{2}}{2}]\\(\frac{3+x_{2} }{2} , \frac{5+y_{2} }{2})\\\frac{3+x_{2} }{2}=1 , \frac{5+y_{2} }{2}=1\\3 + x_{2} = 2 , 5 + y_{2} = 2\\x_{2} = -1 , y_{2} = -3$

C(-1,-3)

M[1,1]=                                     [Diagonals bisect each other]

$[\frac{x+1}{2} , \frac{y+7}{2}]\\\frac{x+1}{2}=1 , \frac{y+7}{2}=1\\x+1=2 , y+7=2\\x=1, y=-5$

D(1,-5)

hence,

A (3,5), B (1,7) ,C(-1,-3),D(1,-5)