Question

The midpoint of the line segment A(2a,4) and B(-2,3b) is C(1,2a+1). Find the value of a and b.

Answer 1

Answer:

$The \: points \: are \: A \: (2a, 4) \: and \: B \: (-2, 3b).</p><p> \\ </p><p>Let  \: C ( 1,2a + 1) \: be \: the \: mid-point \: of \: AB. \: Then:</p><p> \\ </p><p>x=x1+x22,y=y1+y22</p><p> \\ </p><p>⇒1=2a(-2)2,2a+1=4+3b2</p><p> \\ </p><p>⇒2=2a-2,4a+2=4+3b</p><p> \\ </p><p>⇒2a -2+2, 4a -3b = 4-2</p><p> \\ </p><p>⇒a=42,4a-3b=2</p><p> \\ </p><p>⇒ a =2, 4a -3b =2</p><p> \\ </p><p>Putting \: the \: value \: of \: a \: in \: the \: equation \: 4a +3b =2 , \: we \: get:</p><p> \\ </p><p>4(2) - 3b =2</p><p> \\ </p><p>⇒ -3b = 2-8=-6</p><p> \\ </p><p>⇒b=63=2</p><p> \\ </p><p>Therefore,  a =2  and  b= 2 </p><p></p><p>$

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