Question

In what ratio does the x axis divide the line segment joining (-4,-6)&(-1,7)?
Find the coordinates of points of division

Answer 1

Let x-axis divides the line segment joining (–4, –6) and (–1, 7) at the point P in the ratio 1 : k.

Now, coordinates of point of division P are

x coordinate = (-1 - 4k) / (k + 1)

y coordinate = (7 - 6k) / (k + 1)

Since P lies on x-axis, therefore y coordinate = 0

(7 - 6k) / (k + 1) = 0

7 - 6k = 0

k = 7/6

Hence, the ratio is 1:7/6 = 6:7

Now, the coordinates of P are (-34/13, 0)

Answer 2

Let x-axis divides the line segment joining  (– 4, – 6) and (– 1, 7) at the point P in the ratio  1 : k.

Now, coordinates of point of division P are

$\bf\huge\frac{-1-4k}{k+1} , \frac{7-6k}{k+1}$

Since P lies on x-axis

$\bf\huge\frac{7-6k}{k+1} = 0$

7 - 6k = 0

$\bf\huge k=\frac{7}{6}$

Hence the ratio is,

1 : $\bf\huge\frac{7}{6}$ = 6 : 7

Now, the coordinates of P are ($\bf\huge\frac{-34}{13} , 0$)