Question

Determine the distance between the lines : 6x + 8y – 45 = 0 and 3x + 4y – 5 = 0.

Solution

Correct option is

3.5

Note that, two lines are parallel as their slopes are equal.

Distance between two parallel lines Ax + By + C1 = 0 and

Ax + By + C2 = 0 is given by:      

                     

To use this result, write the given equations as:  

               6x + 8y – 45 = 0                     …. (i)  

and            6x + 8y – 10 = 0                    … (ii)

i.e. making the coefficient of xy same in respective equations 

The distance between the lines

                   

SIMILAR QUESTIONS

Q1

Find the slope (m), intercepts on X axis, intercept on Y axis of the line 3x+ 2y – 12 = 0. Also trace the line on XY plane.

Q2

Given the triangle A (10, 4), B(–4, 9), C(–2, 1), find the equation of median through B.

Q3

Find the equation of the straight line passing through the points (3, 3) and (7, 6). What is the length of the portion of the line intercepted between the axes of the coordinates.

Q4

Given the triangle with vertices A (–4, 9), B (10, 4), C (–2, –1). Find the equation of the altitude through A.

Q5

Find the equation of perpendicular bisector of the line joining the points (1, 1) and (2, 3). 

Q6

Find the coordinates of the foot of the perpendicular from the point (2, 3) on the line y = 3x + 4.

Q7

Find the equation of the line passing through (ab) and parallel to px +qy + 1 = 0.  

Q8

Find the equation of the line perpendicular to 3x + 4y + 1= 0 and passing through (1, 1).

Q9

Find the distance of line h (x + h) + k (y + k) = 0 from the origin.

Q10

The algebraic sum of the perpendicular distances from A(x1y1), B(x2,y2) and C(x3y3) to a variable line is zero, then the line passes through: