Question

Determine the ratio in which y – x + 2 = 0 divides the line joining (3, –1) and (8, 9).

Solution

Correct option is

2 : 3

 

Suppose the line y – x + 2 = 0 divides the line segment joiningA(3 –1) and B(8, 9) in the ratio λ : 1 at point P, then the coordinates of the point P are 

But P lies on y – x + 2 = 0 therefore 

       

     

So, the required ratio is 2/3 : 1, i.e., 2 : 3 (internally) since here λ is positive.

 

SIMILAR QUESTIONS

Q1

Find the polar coordinates of the points whose cartesian coordinates are (–3, 4)

Q2

Transform the equation  into cartesian form.

Q3

Transform the equation  into polar form.

Q4

 

Find the distance between the points

            

where a > 0.

Q5

An equilateral triangle has one vertex at the point (0, 0) and another at . Find the coordinates of the third vertyex. 

Q6

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

Q7

Find the circumcentre of the triangle whose vertices are (–2, –3), (–1, 0) and (7, –6). Also find the radius of the circumcircle.

Q8

Find the coordinates of the point which divides the line segment joining the points (5, –2) and (9, 6) in the ratio 3 : 1.

Q9

Find the length of median through A of a triangle whose vertices are A(–1, 3), B(1, – 1)and C(5, 1).

Q10

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (–1, 2) and (2, 5). Then find the coordinates of the fourth vertex.