Question

find the ratio in which the line segment joining the points (-3,10) and (6,-8) is divided by the x axis. Also find the coordinates of the point of division ​

Answer 1

Answer:coordinates 2,0 ratio: 5/4:1

Step-by-step explanation:

Answer 2

The division ratio is 5:4 and coordinates of the point of division ​are (2,0).

Step-by-step explanation:

Let x-axis divide the line segment joining (-3,10) and (6,-8) in m:n.

Point on x-axis is (a,0)

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 sections formula the y-coordinate of point p is

$y-coordinate=\dfrac{m(-8)+n(10)}{m+n}$

$0=\dfrac{-8m+10n}{m+n}$

$0=-8m+10n$

$8m=10n$

$\dfrac{m}{n}=\dfrac{10}{8}$

$\dfrac{m}{n}=\dfrac{5}{4}$

Therefore, x-axis divide the line segment joining (-3,10) and (6,-8) in 5:4.

Using sections formula the x-coordinate of point p is

$x-coordinate=\dfrac{5(6)+4(-3)}{5+4}$

$x-coordinate=\dfrac{18}{9}$

$x-coordinate=2$

Therefore, the division ratio is 5:4 and coordinates of the point of division ​are (2,0).

#Learn more

In what ratio does x axis divide the line segment joining p (-4 -6) and q (-1,7).also find the coordinates of the point of division.

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