Question

The line segment joining the points a(3,2) and b(5,1) is divided at the point p in the ratio 1:2 and p lies on line 3x-18+k=0. Find the value of k

Answer 1

Answer:k=7

Step-by-step explanation:

Internal division formula for x co-ordinate of p is mx2+nx1/m+n

So, x-coordinate of p is

x=1*5+2*3/2+1=11/3

Substituting x in equation 3x^2-18+k=0

3*11/3-18+k=0

11-18+k=0

So k=7

Answer 2

The value of k would be 7.

Step-by-step explanation:

Since, by the segment formula,

If a line with end points $(x_1, y_1)$ and $(x_2, y_2)$ is divided by a point in the ratio of m : n,

Then the coordinates of the point,

$(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

Here, $x_1=3, y_1=2, x_2=5, y_2=1, m = 1, n = 2$

Thus, the coordinates of point p,

$(\frac{1\times 5+2\times 3}{1+2}, \frac{1\times 1+2\times 2}{1+2})$

$(\frac{5+6}{3}, \frac{1+4}{3})$

$(\frac{11}{3}, \frac{5}{3})$

Now, point p passes through line 3x-18+k=0.

So, it will satisfy the line,

$3(\frac{11}{3})-18+k=0$

$11-18+k=0$

$-7+k=0$

$\implies k = 7$

#Learn more :

The line segment joining the points A(4,-3) and B(4,2) is divided by the point P such that AP:AB = 2:5. find the coordinates of P using section formula.

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