2. Find the equation of the line containing the points (2, -3) and (0, -3).
Answers
The two lines are
5x - 2y + 14 = 0 ...(i)
2y = 8 - 7x ...(ii)
Now, putting the value 2y = 8 - 7x in (i), we get
5x - (8 - 7x) + 14 = 0
⇒ 5x - 8 + 7x + 14 = 0
⇒ 12x + 6 = 0
⇒ 12x = - 6
⇒ x = - 6/12
⇒ x = - 1/2
Putting x = - 1/2 in (ii), we get
2y = 8 - 7 (- 1/2)
⇒ 2y = 8 + 7/2
⇒ 2y = (16 + 7)/2
⇒ 2y = 23/2
⇒ y = 23/4
So, the intersection of the lines (i) and (ii) is
(- 1/2, 23/4).
Therefore, the line passing through the points (2, - 6) and (- 1/2, 23/4) be
{y - (- 6)}/(- 6 - 23/4) = (x - 2)/{2 - (- 1/2)}
⇒ (y + 6)/(- 47/4) = (x - 2)/(5/2)
⇒ 5/2 (y + 6) = (- 47/4) (x - 2)
⇒ (5y + 30)/2 = -47 (x - 2)/4
⇒ 4 (5y + 30)/2 = - 47 (x - 2)
⇒ 2 (5y + 30) = - 47x + 94
⇒ 10y + 60 = - 47x + 94
⇒ 47x + 10y = 94 - 60
⇒ 47x + 10y = 34
So, the required line is
47x + 10y = 34.
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