Question

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

Answer 1

since x axis divides the line,y coordinate=0

Let ratio be k:1

Use formula m1y2+m2y1/m1 +m2

k×7+1×-6/k+1=0

7k-6=0

7k=6

k=6/7

Req ratio =6:7

Answer 2

x-axis divide the line segment joining p (-4 -6) and q (-1,7) is 6:7.  The coordinates of the point of division are $(-\dfrac{34}{17},0)$.

Step-by-step explanation:

Let x-axis divide the line segment joining p (-4 -6) and q (-1,7) 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

$y-coordinate=\dfrac{m(7)+n(-6)}{m+n}$

$0=\dfrac{7m-6n}{m+n}$

$0=7m-6n$

$-7m=-6n$

$\dfrac{m}{n}=\dfrac{-6}{-7}$

$\dfrac{m}{n}=\dfrac{6}{7}$

Therefore, x-axis divide the line segment joining p (-4 -6) and q (-1,7) is 6:7.

Using sections formula the x-coordinate of point p is

$x-coordinate=\dfrac{6(-1)+7(-4)}{6+7}$

$x-coordinate=\dfrac{-34}{13}$

Therefore, the coordinates of the point of division are $(-\dfrac{34}{17},0)$.

#Learn more

The point p which divides the line segment joining points a(2,-5) and b(5,2) in the ratio 2:3 lies in which quadrant.

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