One day three friends akash aditya and manoj went to children park to play some game while playing at one moment akash is at point p aditya is at point a and manoj is at point b
Answers
The coordinates of P are ( 5 , 4) or ( -1 , 6) and Aakash Distance from Aditya & Manoj = 2√5 m
Step-by-step explanation:
Aditya point A ( 1 , 2)
Manoj point B ( 3 , 8)
Aakash Distance from Aditya & Manoj are equal
Let say coordinate of P = (x , y)
=> (x - 1)² + (y -2)² = (x - 3)² + (y - 8)²
=> x² - 2x + 1 + y² -4y + 4 = x² - 6x + 9 + y² - 16y + 64
=> 4x + 12y = 68
=> x + 3y = 17
Area of Triangle PAB P(x , y) A ( 1 , 2) , B ( 3 , 8)
= (1/2)| x(2 - 8) + 1 (8 - y) + 3(y - 2)|
= (1/2)| -6x + 8 - y + 3y - 6|
= (1/2) | -6x + 2y + 2|
= -3x + y + 1 or 3x - y - 1
-3x + y + 1 = 10
=> -3x + y = 9
x + 3y = 17
=> y = 6 , x = - 1
3x - y - 1 = 10
=> 3x- y = 11
x + 3y = 17
=> x = 5 & y = 4
Aakash Distance from Aditya & Manoj = √ (5 - 1)² + (4-2)² = √(5 - 3)² + (4 - 8)² = √20 = 2√5
or √ (-1 - 1)² + (6-2)² = √(-1 - 3)² + (6 - 8)² = √20
the coordinates of P are ( 5 , 4) or ( -1 , 6)
Aakash Distance from Aditya & Manoj = √20 m
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