Question

Find the ratio in which the line segment joining P(x1,y1) and Q(x2,y2) is divided by x- axis.

Answer 1

Answer:

The Ratio is $-y_1\,:\,y_2$.

Step-by-step explanation:

Given: Two Points $(x_1,y_1)\:and\:(x_2,y_2)$

To find: Ratio in which line joining given point is divided by x-axis

Line joining is divided by x-axis.

Let the point on x-axis be ( x , 0 )

Also, let the ratio be k : 1

Now we use Section formula,

Coordinate of point which divide Two given point in ratio m : n is given by,

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

Now using this formula we get,

$(x,0)=(\frac{kx_2+1\times x_1}{k+1},\frac{ky_2+1\times y_1}{k+1})$

Equate y coordinates,

$0\:=\:\frac{ky_2+y_1}{k+1}$

$ky_2+y_1\:=\:0$

$ky_2\:=\:-y_1$

$k\:=\:\frac{-y_1}{y_2}$

$\implies k\,:\,1\:=\:\frac{-y_1}{y_2}\,:\,1$

$k\,:\,1\:=\:-y_1\,:\,y_2$

Therefore, The Ratio is $-y_1\,:\,y_2$.

Answer 2

$\boxed{\bf{\red{\bigstar Answer: }}}$

• The line is divided by x axis
• So it's y co-ordinate is 0
• Suppose the Midpoint is (x, 0)
• $\frac{my2 + ny1}{m + n} = 0$
• $my2 + ny1 = 0$
• $my2 = - ny1$
• $\frac{m}{n} = \frac{ - y1}{y2}$