Points A(3,1),B (5,1),C(a,b),D(4,3) are vertics of parallelogram ABCD find the values of a and b

Points A(3,1),B (5,1),C(a,b),D(4,3) are vertics of parallelogram ABCD

1.	Points A(3,1),B (5,1),C(a,b),D(4,3) are vertics of parallelogram ABCD find the values of a and b
Answer» Given\xa0A(3, 1), B(5, 1), C(a, b) and D(4, 3) are the vertices of\xa0parallelogram.We know that, Diagonals of parallelogram bisect each other{tex}\\therefore{/tex}\xa0{tex}\\left(\\frac{3+a}{2}, \\frac{1+b}{2}\\right){/tex}\xa0=\xa0{tex}\\left(\\frac{5+4}{2}, \\frac{1+3}{2}\\right){/tex}Equating x and y terms, we get3 + a = 9 and 1 + b = 4a = 6 and b = 3Therefore,\xa0a = 6, b = 3