मराठी

The Line Segment Joining the Points (−3, −4) and (1, −2) is Divided by Y-axis in the Ratio

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 1 : 3

  •  2 : 3

  • 3 : 1

  •  3 : 2

MCQ
Advertisements

उत्तर

3 : 1

Let the points (−3, −4) and (1, −2) be divided by y-axis at (0,t) in the ratio m:n.

\[\therefore \left( \frac{m - 3n}{m + n}, \frac{- 2m - 4n}{m + n} \right) = \left( 0, t \right)\]

\[\Rightarrow 0 = \frac{m - 3n}{m + n}\]

\[ \Rightarrow m: n = 3: 1\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 23: The straight lines - Exercise 23.21 [पृष्ठ १३४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 23 The straight lines
Exercise 23.21 | Q 13 | पृष्ठ १३४

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).


Find the distance between parallel lines  l (x + y) + p = 0 and l (x + y) – r = 0


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


Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.


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°.


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 (2, 3) from the line 2x − 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.


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.


The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.


Find the perpendicular distance of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ) from the origin.


What are the points on X-axis whose perpendicular distance from the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] is a ?


Show that the product of perpendiculars on the line \[\frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1\]  from the points \[( \pm \sqrt{a^2 - b^2}, 0) \text { is }b^2 .\]


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 \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .

 


Determine the distance between the pair of parallel lines:

4x + 3y − 11 = 0 and 8x + 6y = 15


Find the equation of two straight lines which are parallel to + 7y + 2 = 0 and at unit distance from the point (1, −1).

Answer 3:


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 


Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y+ 5 = 0, whose distance from the point(3, 2) is 7/5.


Write the value of θ ϵ \[\left( 0, \frac{\pi}{2} \right)\] for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.


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


L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through


Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is


The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid 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 ______.


The shortest distance between the lines

`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and

`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is


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


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 distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.


Find the length of the perpendicular drawn from the point P(3, 2, 1) to the line `overliner = (7hati + 7hatj + 6hatk) + λ(-2hati + 2hatj + 3hatk)`


The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is ______units.


The point of intersection of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11, and y =12 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×