Advertisements
Advertisements
Question
The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio
Options
1 : 3
2 : 3
3 : 1
3 : 2
Advertisements
Solution
3 : 1
Let the points (−3, −4) and (1, −2) be divided by y-axis at (0,t) in the ratio m:n.
\[\therefore \left( \frac{m - 3n}{m + n}, \frac{- 2m - 4n}{m + n} \right) = \left( 0, t \right)\]
\[\Rightarrow 0 = \frac{m - 3n}{m + n}\]
\[ \Rightarrow m: n = 3: 1\]
APPEARS IN
RELATED QUESTIONS
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Find the points on the x-axis, whose distances from the `x/3 +y/4 = 1` are 4 units.
What are the points on the y-axis whose distance from the line `x/3 + y/4 = 1` is 4 units.
Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).
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.
If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y+ 7 = 0 is always 10. Show that P must move on a line.
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.
Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.
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.
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 of intersection of the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 from the line 8x + 6y + 5 = 0.
Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]
What are the points on y-axis whose distance from the line \[\frac{x}{3} + \frac{y}{4} = 1\] is 4 units?
If sum of perpendicular distances of a variable point P (x, y) 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:
8x + 15y − 34 = 0 and 8x + 15y + 31 = 0
Determine the distance between the pair of parallel lines:
y = mx + c and y = mx + d
Find 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
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.
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 distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.
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.
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
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
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
The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.
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 ______.
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.
If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.
The distance between the lines y = mx + c1 and y = mx + c2 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 |
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 distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0 is `a/b`. Value of a + b is ______.
