5. Find the co-ordinates of a point P on y-axis so
that PA = PB where A = (-2, 4) and B = (-5, -3).
Answers
Given:-
PA = PB
A = (-2, 4) = (x1, y1) and B = ( -5, -3) = (x2, y2)
To Find:-
co-ordinates of point P on y axis.
Solution:-
Point p is on y axis.
•°• coordinate of point P should be 0 and y i.e (0, y)
°•° PA = PB •°• PA² = PB²
- By Distance formula
(0 - (-2))² + (y - 4)² = (0 - (-5))² + (y - (-3))²
(0 + 2)² + (y - 4)² = (0 + 5)² + (y + 3)²
2² + (y² - 8y + 16) = 5² + (y² - 6y + 9)
4 + y² - 8y + 16 = 25 + y² - 6y + 9
y² - 8y + 20 = y² - 6y + 34
- 8y + 20 = -6y + 34
- 8y + 6y = 34 - 20
- 2y = 14
y = 14/-2 = -7
•°• y = -7
Answer:- The co-ordinate of point P on y axis is 0 and -7, i.e. P = (0, -7).
Given ,
- A = (-2,4) and B = (-5,-3)
- The coordinate of point P is on the y axis
- The distance between point P and A is equal to the point P and B
Let , The coordinate of P be " (0 , y)
We know that ,
The distance between two points is given by
According to the question ,
Therefore ,
The coordinate of point P is (0 , -7)