Find The Sum Of The Abscissas Of All The Points On The Line x + y = 4 That Lie At A Unit Distance From The Line 4x + 3y – 10 = 0.

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Question

Find the sum of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y – 10 = 0.

Solution

Correct option is

–4

 

Any point on the line x + y = 4 can be taken as (x1, 4 – x1). As it is at a unit distance from the line 4x + 3y – 10 = 0, we get  

         

  

  

⇒     x1 = 3 or –7   

∴ Required sum = 3 – 7 = –4.

Testing

SIMILAR QUESTIONS

Q1

Find the distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along the line 2x – 2y + 5 = 0.

Q2

The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anticlockwise direction through an angle of 15o. Find the equation of the line in the new position. If B goes to C in the new position, what will be the coordinates of C 

Q3

The centre of a square is at the origin and one vertex is A(2, 1). Find the coordinates of other vertices of the square. 

Q4

The extremities of the diagonal of a square are (1, 1), (–2, –1). Obtain the other two vertices and the equation of the other diagonal.  

Q5

Are the points (2, 1) and (–3, 5) on the same or opposite side of the line 3x – 2y + 1 = 0?

Q6

Is the point (2, –7) lie on origin side of the line 2x + + 2 = 0?

Q7

A straight canal is at a distance of  km from a city and the nearest path from the city to the canal is in the north-east direction. Find whether a village which is at 3 km north and 4 km east from the city lies on the canal or not. If not, then on which side of the canal is the village situated? 

Q8

 

Find the general equation of the line which is parallel to

3x – 4y + 5 = 0. Also find such line through the point (–1, 2).

Q9

Find the general equation of the line which perpendicular to x + y + 4 = 0. Also find such line through the point (1, 2).   

Q10

If p and p’ are the length of the perpendiculars from the origin to the straight line whose equations are , then find the value of 4p2 + p2.