Question

Find the distance between lines, 3 x+y-12=0 and 3 x+y-4=0

a. 13.6
b. 54.2
c. 2.53
d. 7.54

Answer 1

To find the distance between the parallel lines 3x + y - 12 = 0 and 3x + y - 4 = 0, we use the formula for the distance d between two parallel lines resulting in an approximate distance of 2.53.

Step-by-step explanation:

To find the distance between two parallel lines of the form 3x + y - C = 0, where C is a constant, we can use the formula for the distance d between two parallel lines:

d = |C1 - C2| / sqrt(a^2 + b^2)

In the given lines, 3x + y - 12 = 0 and 3x + y - 4 = 0, the coefficients a and b for x and y are 3 and 1, respectively. The constants are C1 = 12 and C2 = 4.

Plugging the values into the formula:

d = |12 - 4| / sqrt(3^2 + 1^2)
d = 8 / sqrt(10)
d = 8 / sqrt(10) * sqrt(10) / sqrt(10)
d = 8\sqrt{10} / 10
d ≈ 2.53 (to two decimal places)

So, the correct answer to the distance between the lines is option (c) 2.53.