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;
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-
Answers
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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