Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0.
Given:
4x + y − 1 = 0 … (1)
7x − 3y − 35 = 0 … (2)
Concept Used:
Point of intersection of two lines.
Explanation:
Solving (1) and (2) using cross - multiplication method:
⇒ x = 2 ,y = - 7
Thus, the point of intersection of the given lines is (2, - 7).
So, the equation of the line joining the points (3, 5) and (2, - 7) is
⇒ y - 5 = 12x - 36
⇒ 12x – y – 31 = 0
Hence, the required equation of line is 12x – y – 31 = 0