Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x – 4y + 11 = 0 from the line 8x + 6y + 5 = 0.
Given:
Lines 2x + 3y = 21 and 3x – 4y + 11 = 0
To find:
The distance of the point of intersection of the lines 2x + 3y = 21 and 3x – 4y + 11 = 0 from the line 8x + 6y + 5 = 0.
Concept Used:
Distance of a point from a line.
Explanation:
Solving the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 we get:
⇒ x = 3, y = 5
So, the point of intersection of 2x + 3y = 21 and 3x − 4y + 11 = 0 is (3, 5).
Now, the perpendicular distance d of the line 8x + 6y + 5 = 0 from the point (3, 5) is
d
Hence, distance is .