Question

Find the distance between the lines 3x+4y+5=0 and 6x+8y=25​

Answer 1

Answer: The distance between the lines is 3½ units.

Step-by-step explanation:

Given equations of lines are:

3x+4y+5=0____(i)

6x+8y=25 Or 3x+4y+(-25/2)=0____(ii)

Let us check whether the given lines are parallel or not.

From (i),

3x+4y=(-5)

⇒ 4y=(-3)x - 5

⇒ y = (-3/4)x - (5/4)

Here, slope = m1 = -3/4

From (ii),

6x+8y=25

⇒ 8y=(-6)x + 25

⇒ y = (-6/8)x + (25/8)

⇒ y = (-3/4)x + (25/8)

Here, slope = m2 = -3/4

We know, if the slope of the two lines are equal then they are parallel to each other.

Now, by comparing with the standard form of parallel lines equations, we get:

A = 3, B = 4, C1 = 5, C2 = -25/2

d = |C1 - C2|/√(A² + B²)

= |5+25/2|/√(9+16)

= |10+25|/2√25

= |35|/(2×5)

= 35/10

= 7/2

= 3½

∴The distance between the given lines is 3½ units.