Q8 of 157 Page 757

If the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k.

Given that point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3.


∴ m:n = 2:3


Recall that if (x,y) ≡ (a,b) then x = a and y = b


Let (x,y) ≡ (k,4)


(x1,y1) ≡ (2,6)


and, (x2,y2) ≡ (5,1)


Now, Using Section Formula-



On dividing numerator and denominator of R.H.S by n, we get-





∴ k = (16/5)


Thus the value of k is (16/5).


More from this chapter

All 157 →
6

Prove that the diagonals of a rectangle ABCD with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6) are equal and bisect each other.

 7

Find the lengths of the medians AD and BE of ΔABC whose vertices are A(7, -3), B(5, 3) and C(3, -1).

 9

Find the point on x-axis which is equidistant from points A(-1, 0) and B(5, 0).

 10

Find the distance between the points .