Q22 of 149 Page 14

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.

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



By section formula,


x = , y =


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


x1 = , y1 =


∴ 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


More from this chapter

All 149 →
20

If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.

 21

If the coordinates of the mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7), find its vertices.

 23

If the points (-2 , -1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

 24

The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.