Question

The line segment joining the points (1,2) and (k,1) is divided by the line 3x+4y-7=0 in the ratio 4:9 then k is

Answer 1

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Answer 2

Answer:

The value of k is -2.

Step-by-step explanation:

It is given that line segment joining the points (1,2) and (k,1) is divided by the line 3x+4y-7=0 in the ratio 4:9.

Section formula:

If a point divides a line segment in m:n whose end points are $(x_1,y_1)$ and $(x_2,y_2)$, then the coordinates of that point are

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

Using section formula the point of intersection is

$(\frac{(4)(k)+(9)(1)}{4+9},\frac{(4)(1)+(9)(2)}{4+9})$

$(\frac{4k+9}{13},\frac{4+18}{13})$

$(\frac{4k+9}{13},\frac{22}{13})$

The point of intersection lies on the line 3x+4y-7=0. It means 3x+4y-7=0 must be satisfied by the point $(\frac{4k+9}{13},\frac{22}{13})$.

$3x+4y-7=0$

$3(\frac{4k+9}{13})+4(\frac{22}{13})-7=0$

$\frac{12k+27}{13}+\frac{88}{13}-7=0$

$\frac{12k+27}{13}-\frac{3}{13}=0$

$\frac{12k+27}{13}=\frac{3}{13}$

$12k+27=3$

$12k=-27+3$

$12k=-24$

Divide both sides by 12.

$k=-\frac{24}{12}$

$k=-2$

Therefore the value of k is -2.