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 $(3,1),(-7,11)$.
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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