One day, three friends Akash, Aditya and Manoj......
Answers
Answer:
(-1,6)
Step-by-step explanation:
let P be (x,y)
since the distance are equal,
distance AP=distance BP
using distance formula,
root[ (x-1)^2 +(y-2)^2 ]=root [ (x-3)^2 + (y-8)^2 ]
on squaring,
and simplifying we get,
2 x+12 y=70
=> x+6 y=35 .........1
since area =10 sq.units
area=1/2 [1(8-y)+3(y-2)+x(2-8)] =10
when you simplify the equation,
6 x-2 y=-18 ................2
solving 1 and 2,
we get
x=-1 and y=6
hence the coordinate is (-1,6)
hope it helps.....
The coordinates of P are ( 5 , 4) or ( -1 , 6) and Aakash Distance from Aditya & Manoj = √20 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
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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