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 .