An exhibition is being organised in the school premises to highlight "Swatchebih Bharat Abhiyan' and 'Say no to plastic'. Material concerning these is displayed at the positions represented by the points A(-4,0) and B(4,0). A spot light is placed at a point represented by P(a, b) such that A, B and P are equidistant from each other. (i) Help me in finding the position of point P by finding the values of a and b. (ii) The distance of point P from line segment AB.
Answers
The distance of point P from line segment AB is 4√3
Point = A = ( - 4, 0) (Given)
Point = B = ( 4, 0) (Given)
Point = P ( a , b) (Given)
Now,
PA = PB = AB
Therefore,
AB = √(4 -(-4))² + (0 - 0)²
= 8
PA = PB
= √(a + 4)² + b² = √(a - 4)² + b²
= (a + 4)² + b² = (a - 4)² + b²
= a² + 16 + 8a = a² + 16 - 8a
= 16a = 0
a = 0/16 = 0
Now, PA = PB = √4² + b²
√4² + b² = 8
= 16 + b² = 64
= b² = 48
= b = ± 4√3
Thus, the distance of point P from the line segment AB is 4√3
Answer:An exhibition is being organised in the school premises to highlight "Swatchebih Bharat Abhiyan' and 'Say no to plastic'. Material concerning these is displayed at the positions represented by the points A(-4,0) and B(4,0). A spot light is placed at a point represented by P(a, b) such that A, B and P are equidistant from each other. (i) Help me in finding the position of point P by finding the values of a and b. (ii) The distance of point P from line segment AB.
Step-by-step explanation:
answer :
A = ( - 4, 0) (Given)
B = ( 4, 0) (Given)
Point P ( a , b) (Given)
Now,
PA = PB = AB
Therefore,
AB = √(4 -(-4))² + (0 - 0)²
= 8
PA = PB
= √(a + 4)² + b² = √(a - 4)² + b²
= (a + 4)² + b² = (a - 4)² + b²
= a² + 16 + 8a = a² + 16 - 8a
= 16a = 0
a = 0/16 = 0
Now, PA = PB = √4² + b²
√4² + b² = 8
= 16 + b² = 64
= b² = 48
= b = ± 4√3
Thus, the distance of point P from the line segment AB is 4√3