Question

in what ratio is the line segment joining the point - 2, - 3 and 3, 7 divided by the y axis also find the coordinates of the point of division​

Answer 1

The required ratio is 2:3. The coordinates of the point of division​ are (0,1).

Step-by-step explanation:

Let y axis divide the line segment joining the point (-2,-3) and (3,7) in m:n.

The coordinates of the point of division​ is (0,y).

Section formula:

If a point divides a line segment in m:n whose end points are  and , then the coordinates of that point are

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

Using section formula the coordinates of the point of division​ are

$(\dfrac{m(3)+n(-2)}{m+n},\dfrac{m(7)+n(-3)}{m+n})$

$(\dfrac{3m-2n}{m+n},\dfrac{7m-3n}{m+n})$

The coordinates of the point of division​ is (0,y).

$(\dfrac{3m-2n}{m+n},\dfrac{7m-3n}{m+n})=(0,y)$

On comparing x-coordinate we get

$\dfrac{3m-2n}{m+n}=0$

$3m-2n=0$

$3m=2n$

$\dfrac{m}{n}=\dfrac{2}{3}$

The required ratio is 2:3.

y-coordinate of point of division​ is

$y=\dfrac{7m-3n}{m+n}$

Substitute m=2 and n=3 in the above equation.

$y=\dfrac{7(2)-3(3)}{(2)+(3)}$

$y=\dfrac{14-9}{5}$

$y=\dfrac{5}{5}$

$y=1$

Therefore, the coordinates of the point of division​ are (0,1).

#Learn more

The point P dividing the line segment joining The point A(2,3)and B(10,-6) in the ratio 3:2.

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