quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (– , – ), ( , ), (– , ), (– , ) (ii) (– , ), ( , ), ( , ), (– , – ) (iii) ( , ), ( , ), ( , ), ( , ) . Find the point on the x -axis which is equidistant from ( , – ) and (– , ). . Find the values of y for which the distance between the points P( , – ) and Q( , y ) is units.
. If Q( , ) is equidistant from P( , – ) and R( x , ), find the values of x . Also find the distances QR and PR. .
Find a relation between x and y such that the point ( x , y ) is equidistant from the point ( , ) and (– , ). . Section Formula Let us recall the situation in Section . .
Suppose a telephone company wants to position a relay tower at P between A and B is such a way that the distance of the tower from B is twice its distance from A. If P lies on AB, it will divide AB in the ratio : (see Fig. . ).
If we take A as the origin O, and km as one unit on both the axis, the coordinates of B will be ( , ). In order to know the position of the tower, we must know the coordinates of P. How do we find these coordinates? Let the coordinates of P be ( x , y ).
Draw perpendiculars from P and B to the x -axis, meeting it in D and E, respectively. Draw PC perpendicular to BE. Then, by the AA similarity criterion, studied in Chapter , POD and BPC are similar. Therefore , OD OP PC PB , and PD OP BC PB x and y These equations give x = and y = .
You can check that P( , ) meets the condition that OP : PB = : . Now