Question

Q 3. Point P ( a / 8 , 4 ) is the mid point of the line segment joining the points A ( - 5, 2) and B ( 4, 6 ), the value of a is ​

Answer 1

Answer:

- 4

Step-by-step explanation:

Using mid point formula,

=> (-5+4/2 , 2+6/2) = mid point of AB

=> (-1/2, 8/2) = (a/8, 4)

=> (-1/2, 4) = (a/8, 4)

=> -1/2 = a/8

=> -4 = a

If you haven't studied this, use distance formula :

=> distance b/w A and P = distance b/w B and P

=> √{(a/8 - (-5))² + (4 - 2)² = √{(a/8 - 4)² + (4 - 6)²}

=> (a/8 + 5)² + 2² = (a/8 - 4)² + 2²

=> (a/8 + 5)² = (a/8 - 4)²

=> a/8 + 5 = ± (a/8 - 4)

=> a/8 + 5 = - a/8 + 4 {neglect +ve}

=> a/8 + a/8 = 4 - 5

=> 2a/8 = - 1

=> a = - 4