# The line segment joining the points P (3, 3) and Q (6, - 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Given: points P (3, 3) and Q (6, - 6).

Line 2x + y + k = 0

To find: The value of k.

Formula Used:

section formula:

If point P (x, y) divides the line segment A(x1, y1) and B(x2,y2)

Then the coordinates of P are:

Explanation:

Here, given points are P (3, 3) and Q (6, - 6) which is trisected at the points A (x1 , y1) and B(x2 , y2) such that A is nearer to P.

By section formula,

For point A (x1, y1) of PQ, where m = 2 and n = 1,

x1 = 4, y1 = 0

Coordinates of A is (4,0)

It is given that point A lies on the line 2x + y + k = 0.

So, substituting value of x and y as coordinates of A,

2 × 4 + 0 + k = 0

k = - 8

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Section Formula30 mins
Champ Quiz | Previous Year NTSE QuestionsFREE Class
Measuring distance by Distance formula49 mins
Champ Quiz | Distance Formula30 mins
Imp. Qs. on Distance Formula68 mins
Coordinate Geometry Important Questions38 mins
Champ Quiz | Coordinate Geometry Problems38 mins
Quiz | Solving Important Questions on Section Formula54 mins
Important Questions of Coordinate Geometry39 mins
Previous Year RMO Questions43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses