question_answer

The points A, B and C are collinear and \[\text{AB}=\text{BC}\]. If the coordinates of A,B and C are \[(3,a),\] \[(1,3)\] and \[(b,4)\]respectively, then the values of a and b are:                                                                         (CBSE 2013)

A) \[2\ and-1\]

B) \[~1\ and-2\]

C) \[~1\ and\ 2\]

D) \[-~1\ and\ -2\]

Correct Answer: A

Solution :

[a] \[AB=BC\]and A,B and C are collinear.

\[\therefore \] B is the mid-point of AC.

By mid-point formula,

\[(1,3)=\left( \frac{3+b}{2},\frac{a+4}{2} \right)\]

On comparing x and y-coordinates, we get

\[1=\frac{3+b}{2}\Rightarrow 3+b=2\Rightarrow b=-1\]

and\[3=\frac{a+4}{2}\Rightarrow a+4=6\Rightarrow a=2\]

Hence, \[a=2\] and \[b=-1\].