The mid point of the line segment joining (2a, 4)and (-2,3b) is (1,2a+1). The value of a and b is

The mid point of the line segment joining (2a, 4)and (-2,3b) is (1,2a+

1.	The mid point of the line segment joining (2a, 4)and (-2,3b) is (1,2a+1). The value of a and b is
Answer» C(1, 2a + 1) is the midpoint of A(2a, 4) and B(-2, 3b){tex}x = \\frac { x _ { 2 } + x _ { 1 } } { 2 }{/tex}and\xa0{tex}y = \\frac { y _ { 2 } - y _ { 1 } } { 2 }{/tex}{tex}1 = \\frac { - 2 + 2 a } { 2 }{/tex}and\xa0{tex}2 a + 1 = \\frac { 3 b + 4 } { 2 }{/tex}2 = -2 + 2a and 4a + 2 = 3b + 4 ...(1)a = 2 ...(2)Putting a = 2 in (1), we get4\xa0{tex}\\times{/tex}2 + 2= 3b\xa0{tex}\\Rightarrow{/tex}\xa010 - 4 =3b{tex}\\Rightarrow{/tex}\xa03b = 6\xa0{tex}\\Rightarrow{/tex}{tex}b = \\frac { 6 } { 3 } = 2{/tex}Hence, a = 2 and b = 2