7
The point A has coordinates (p, 1) and the point B has coordinates (9, 3p + 1), where p is a constant.
(1) For the case where the distance AB is 13 units, find the possible values of p.
[3]
(ii) For the case in which the line with equation 2x + 3y = 9 is perpendicular to AB, find the value
of p.
Answers
Answered by
5
Answer:
- 11 / 5 , 4 , 3.
Step-by-step explanation:
From the properties of straight lines :
- Slope of a line is given by ( y₂ - y₁ ) / ( x₂ - x₁ ), where ( x₁ , y₁ ) and ( x₂ , y₂ ) are just two points lying the line.
- Distance between two points is √{ ( x₂ - x₁ )^2 + ( y₂ - y₁ )^2 }
According to situation 1 :
⇒ √{ ( 3p + 1 - 1 )^2 + ( 9 - p )^2 } = 13
⇒ ( 3p )^2 + ( 9 - p )^2 = 169
⇒ 9p^2 + 81 + p^2 - 18p = 169
⇒ 10p^2 - 18p + 81 - 169 = 0
⇒ ( 5p + 11 )( p - 4 ) = 0
Possible values are - 11 / 5 or 4.
For situation 2 :
If 2x + 3y = 9 is perpendicular to line AB,
Slope of 2x + 3y = 9 is - 1 / slope of AB.
⇒ - 2 / 3 = - 1 / { ( 3p + 1 - 1 ) / ( 9 - p ) }
⇒ 2 / 3 = ( 9 - p ) / ( 3p )
⇒ 2( 3p ) = 3( 9 - p )
⇒ 6p = 27 - 3p
⇒ 9p = 27
⇒ p = 3
Similar questions