The coordinates of the two points lying on $x + y = 4$ and at a unit distance from the straight line $4x + 3y = 10$ are
- (-3, 1), (7, 11)
- (3, 1), (-7, 11)
- (3, 1), (7, 11)
- (5, 3), (-1, 2)
The Correct Option is B
Solution and Explanation
According to the given condition,
$\left|\frac{4 h+3(4-h)-10}{5}\right|=1$
$\Rightarrow|h+2|=5 $
$\Rightarrow h+2=\pm 5 $
$\Rightarrow \quad h=3,-7$
Hence, required points are $(3,1),(-7,11)$.
Top Questions on Distance of a Point From a Line
- If a point $ P(x, y) $ satisfies the condition that its distance from the point $ (3, -2) $ is equal to its distance from the line $ y = 2x + 1 $, then the locus of point $ P $ is:
- BITSAT - 2025
- Mathematics
- Distance of a Point From a Line
- Find the foot of the perpendicular drawn from the point \( (1, 1, 4) \) on the line \( \frac{x+2}{5} = \frac{y+1}{2} = \frac{z-4}{-3} \).
- CBSE CLASS XII - 2025
- Mathematics
- Distance of a Point From a Line
- Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).
- CBSE CLASS XII - 2025
- Mathematics
- Distance of a Point From a Line
- Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).
- CBSE CLASS XII - 2025
- Mathematics
- Distance of a Point From a Line
- Find the midpoint of the line segment joining the points (3, 4) and (7, -2).
- AP EAPCET - 2025
- Mathematics
- Distance of a Point From a Line
Questions Asked in WBJEE exam
- The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass \( m \) is represented by: \[ y = 2 \sin \left( \frac{\pi}{2} + \phi \right) \, \text{cm} \] The maximum acceleration of the particle is:
- WBJEE - 2025
- simple harmonic motion
- Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day, if she remains stationary on the escalator moving with velocity \( v_2 \), the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be:
- WBJEE - 2025
- Relative Motion
- A force \( \mathbf{F} = ai + bj + ck \) is acting on a body of mass \( m \). The body was initially at rest at the origin. The co-ordinates of the body after time \( t \) will be:
- WBJEE - 2025
- Newtons Laws of Motion
A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( L \) is the length,
- \( \Delta V \) is the potential difference,
- \( \Delta t \) is the time interval.
The dimension of \( X \) is the same as that of:- WBJEE - 2025
- Dimensional Analysis
- Which logic gate is represented by the following combination of logic gates?
- WBJEE - 2025
- Logic gates
Concepts Used:
Distance of a Point From a Line
The length of the perpendicular drawn from the point to the line is the distance of a point from a line. The shortest difference between a point and a line is the distance between them. To move a point on the line it measures the minimum distance or length required.
To Find the Distance Between two points:
The following steps can be used to calculate the distance between two points using the given coordinates:
- A(m1,n1) and B(m2,n2) are the coordinates of the two given points in the coordinate plane.
- The distance formula for the calculation of the distance between the two points is, d = √(m2 - m1)2 + (n2 - n1)2
- Finally, the given solution will be expressed in proper units.
Note: If the two points are in a 3D plane, we can use the 3D distance formula, d = √(m2 - m1)2 + (n2 - n1)2 + (o2 - o1)2.
Read More: Distance Formula