Question

The point ______ lies on the perpendicular bisector of the line segment joining the points A ( -2 , -5 ) and B ( 2 , 5 ) :

Answer 1

Given :-

Two points A ( - 2 , - 5 ) & B ( 2 , 5 )

To Find :-

The Point's Coordinates which lies on the perpendicular bisector Joining A & B

Solution :-

Consider a Line segment with one end A ( - 2 , - 5 ) & ( 2 , 5 )

Construction :- Now , draw the perpendicular bisector Let It be 'NO' . ( See the attachment )

Now , we have to find the coordinates of N as it is the perpendicular bisector of AB . Which implies that , N is the midpoint of AB . So here the concept of Mid Point Formula will be implemented . Which states that For any two Points A & B with coordinates ${ \sf { ( x_{1} , x_{2} ) \:\: and \:\:( x_{2} , y_{2} ) }}$ , the midpoint of AB is given by ;

$\quad \qquad { \bigstar { \underline { \boxed { \red { \bf { \bigg ( \dfrac{x_{1} + y_{1}}{2} , \dfrac{y_{1} + y_{2}}{2} } \bigg ) }}}}}{\bigstar}$

Now using this the coordinates of N are ;

$: \implies { \sf { N(x,y) = { \bigg ( \dfrac{2 - 2}{2} , \dfrac{5 - 5}{2}} \bigg ) }}$

$: \implies { \sf { N(x,y) = { \bigg ( \dfrac{0}{2} , \dfrac{0}{2}} \bigg )}}$

$: \implies { \sf { N(x,y) = (0 , 0 )}}$

Henceforth , Option ( a ) is correct !