Question

A policeman and a thief are equidistant from the jewel box, upon considering jewel box as origin, the position of the policeman is ( 0 , 5 ). If the ordinate of the position of the thief is zero. Then write the coordinates of the position of the thief.

Answer 1

Hint:
We are given that the position of the jewel box is at the origin and the coordinates of the police man to be (0 , 5). We are given that the ordinate of the position of the thief is 0. So let the abscissa of the position of the thief be x.And the coordinate of the position of the thief be Q(x,0). As the police and the thief are equidistant from the jewel box . we get OP = OQ and using the distance formula $\sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $we need to find the value of OP and OQ and equating them we get the value of x.

Complete step by step solution:
We are given that the position of the jewel box is at the origin. Let the position of the jewel box be O (0,0). Now let the position of the police man be P. And we are given the coordinates of the police man to be (0 , 5). Therefore P = (0,5). And we are given that the ordinate of the position of the thief is 0. Ordinate of point is nothing other than its y coordinate and the x coordinate is known as the abscissa. So, let the abscissa of the position of the thief be x
And the coordinate of the position of the thief be Q(x,0)
We are given that the police and the thief are equidistant from the jewel box
That is OP = OQ
Now we can use the distance formula $\sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $ to find OP and OQ
Distance between O(0 , 0) and P(0 , 5)
$
   \Rightarrow OP = \sqrt {{{(0 - 0)}^2} + {{(5 - 0)}^2}} \\
   \Rightarrow OP = \sqrt {{5^2}} = 5units \\
 $
Distance between O(0 , 0) and Q(x , 0)
$
   \Rightarrow OQ = \sqrt {{{(x - 0)}^2} + {{(0 - 0)}^2}} \\
   \Rightarrow OQ = \sqrt {{x^2}} = xunits \\
 $
We know that OP = OQ
$ \Rightarrow 5 = x$
Therefore we get the value of x to be 5.

Hence the coordinates of the position of the thief is (5 , 0).

Note:
If the police , thief and the jewel box are in a straight line. As we are given that the police and the thief are equidistant from the jewel box. Then the coordinates of the jewel box is the midpoint of the line joining the coordinates of the police and thief.