Question

28. Two friends start their journey from same place at
location is represented by points A and B or
start his journey from the same place and atte
om same place at same time. After some time their
A and B on the coordinate axes as shown. If third friend
same place and after sometime, its location point P, with
then determine
ze that point A, Pand B are on same straight line.)
respect to the points A and B is represented by the relation
wordinates of point P. (Assume that point A, Pand B are on
-2
-1 0
2;
4;
*
3;
---
-​

Answer 1

Given : Two friends start their journey from same place at same time. location is represented by  points A & B Coordinates in graph A = (-2 , - 2) B = (2 , -4) AP = AB & A , P , B are on straight line

To Find : Coordinate of point P

Solution:

A = (- 2 , - 2)

B = ( 2 , - 4)

Slope of the line

= ( -4 -(-2))/(2 -(-2))

= =2/4

= -1/2

line

y = -x/2 + c

- 2 = 1 + c

=> c = -3

=> y = -x/2 -3

=> 2y = -x - 6

=> x = -(2y + 6)

AB = √(2 -(-2))² + (-4 -(-2))²

=> AB = √20

AP = √(x -(-2))² + (y - (-2))²

√(x +2)² + (y + 2)² = √20

=> (x +2)² + (y + 2)² = 20

x = -(2y + 6)

=> (-2y + 4)² + (y + 2)² = 20

=> 4(y + 2)² + (y + 2)² = 20

=> 5(y + 2)²  = 20

=> (y + 2)²  = 4

=> y + 2 = ± 2

=> y = 0 ,  - 4

x = -6  ,   2

(2 , - 4)  is B

(- 6 , 0) is P

the coordinates of point  is P (- 6 , 0)

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