English

Determine the Distance Between the Pair of Parallel Lines: 4x + 3y − 11 = 0 and 8x + 6y = 15 - Mathematics

Advertisements
Advertisements

Question

Determine the distance between the pair of parallel lines:

4x + 3y − 11 = 0 and 8x + 6y = 15

Short/Brief Note
Advertisements

Solution

The given parallel lines can be written as
4x + 3y − 11 = 0            ... (1)

\[4x + 3y - \frac{15}{2} = 0\]     ... (2)
Let d be the distance between the given lines.
\[\Rightarrow d = \left| \frac{- 11 + \frac{15}{2}}{\sqrt{4^2 + 3^2}} \right| = \frac{7}{2 \times 5} = \frac{7}{10}\] units

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: The straight lines - Exercise 23.16 [Page 114]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 23 The straight lines
Exercise 23.16 | Q 1.4 | Page 114

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units.


Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.


Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.


Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.


Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x-axis is 15°.


Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan−1 \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .


A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.


A line a drawn through A (4, −1) parallel to the line 3x − 4y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.


Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope 1/2.


Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.


Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.


Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x − 4y+ 8 = 0.


Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.


Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]


If sum of perpendicular distances of a variable point P (xy) from the lines x + y − 5 = 0 and 3x − 2y + 7 = 0 is always 10. Show that P must move on a line.


If the length of the perpendicular from the point (1, 1) to the line ax − by + c = 0 be unity, show that \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .

 


Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.


Find the ratio in which the line 3x + 4+ 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 


If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sin θ, − cos θ) lies on the line y = 2x, then write the value of tan θ.


If the lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent, then write the value of 2abc − ab − bc − ca.


Write the locus of a point the sum of whose distances from the coordinates axes is unity.


The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio


The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is


The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 is


A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) is ______.


If the tangent to the curve y = 3x2 - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are


Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.


Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.


A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.


The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.


The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are

Column C1 Column C2
(a) Parallel to y-axis is (i) λ = `-3/4`
(b) Perpendicular to 7x + y – 4 = 0 is (ii) λ = `-1/3`
(c) Passes through (1, 2) is (iii) λ = `-17/41`
(d) Parallel to x axis is λ = 3

A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×