Question

The midpoints of the line segment joining A(2a,4) and B-2,3b) is M(1,2a+1). Find the values of a and b

Answer 1

Answer:

$a = 2 , b=2$

Step-by-step explanation:

$The \: mid\: point \: M(1,2a+1) \: of\\\: the \:line \: segment \: joining \: the \: points \\\: A(x_{1},y_{1})=(2a,4)\: and\\ \: B(x_{2},y_{2}) = (-2,3b) .$

$\implies M(1,2a+1)= \big(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\big)$

$\implies M(1,2a+1)= \big(\frac{2a-2}{2},\frac{4+3b}{2}\big)\\=\big(\frac{2(a-1)}{2},\frac{4+3b}{2}\big)$

$\implies M(1,2a+1)=\big(a-1,\frac{4+3b}{2}\big)$

$\implies 1= a-1 ; 2a+1=\frac{4+3b}{2}$

$\implies 2 = a ; 2(2a+1)=4+3b$

Substitute a = 2,we get

$\implies a = 2 , 2(4+1)=4+3b$

$\implies a = 2 , 10=4+3b$

$\implies a = 2 , 10-4=3b$

$\implies a = 2 , \frac{6}{3}=b$

$\implies a = 2 , b=2$

Therefore,

$a = 2 , b=2$

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Answer 2

Answer:

hope it helps.

Step-by-step explanation:

my handwriting is not good.

sorry for it.