pls solve................
Answers
Solution :
[ We know that, the median of a triangle always passes through one vertex and the mid-point of the opposite side. ]
The given triangle has three vertices P, Q, R with coordinates (2, 2), (6, - 1), (7, 3) respectively.
Then, the mid-point of the side QR is
( (6 + 7)/2, (- 1 + 3)/2 )
i.e., (13/2, 1)
∴ the median PS passing through the points (2, 2) and (13/2, 1) has an equation
(x - 2)/(2 - 13/2) = (y - 2)/(2 - 1)
⇒ (x - 2)/(- 9/2) = (y - 2)/1
⇒ 2 (x - 2) = - 9 (y - 2)
⇒ 2x - 4 = - 9y + 18
⇒ 2x + 9y = 22
We have to find the parallel line of the median PS : 2x + 9y = 22.
Let us consider the line parallel to PS be
2x + 9y + k = 0 .....(1) ,
where k is arbitrary constant
It is given that (1) no. line passes through the point (1, - 1), so
(2 * 1) + 9 (- 1) + k = 0
⇒ 2 - 9 + k = 0
⇒ k = 7
∴ the required parallel line to PS is
2x + 9y + 7 = 0
⇒ option (d) 2x + 9y + 7 = 0 is correct.