Question

M&N are two points on x &y axis respectively. P(3,2)divides line segment MN in ratio 2:3.find-coordinates of M&N,slope of line MN.

Answer 1

Answer:

The co ordinates of M and N are (5,0) and (0,5)

Slope of the line MN is -1

Step-by-step explanation:

Formula used:

Section formula:

The co ordinates of the point which divides the line segment joining $(x_1,y_1)\:and\:(x_2,y_2)$ internally in the ratio m:n is

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

Slope of the line joining $(x_1,y_1)\:and\:(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$

Let the co ordinates of M and N be

(a,0) and (0,b)

since P(3,2) divides the line joining M and N internally in the ratio 2:3,

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})=(3,2)\\\\(\frac{2(0)+3(a)}{2+3},\frac{2(b)+3(0)}{2+3})=(3,2)\\\\(\frac{3a}{5},\frac{2b}{5})=(3,2)\\\\\frac{3a}{5}=3\\\\\frac{a}{5}=1\\\\a=5\\and\\\\\frac{2b}{5}=2\\\\\frac{b}{5}=1\\\\b=5$

Now,

M(5,0) and N(0,5)

slope of the line MN

$=\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{5-0}{0-5}\\\\=\frac{5}{-5}\\\\=-1$

Answer 2

Answer:

Bit 1 - M (5,0), N(0,5)

Bit 2 - m = - 1