Question

the line segments joinging points (3,4) and (1,-2) is divided by x-axis in the ratio

Answer 1

Answer: The required ratio is 2 : 1

Step-by-step explanation

Let P be the point where the x-axis divides the line segment

Let the ratio be k : 1

The coordinates of point P is (x,0)

{y=0 because P is a point on x-axis so 'y' coordinate of point P is 0}

Therefore,  using the section formula

y = $\frac{1 * 4 + k * -2}{k + 1}$

0  = $\frac{4 -2k}{k + 1}$

0 =  4 - 2k    ( i multiplied k=1 with 0........(k+1) x0 = 0)

-4  =  -2k

-4/-2  = k

  2     =  k

k : 1  =  2 : 1

Therefore k : 1 = 2 : 1

Hope this helps !!!

Cheers!!

Answer 2

Answer:

Ratio = 2:1

Step-by-step explanation:

The equation of line joining the points (3,4) and (1,-2).

$\frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1}$

y-4/-6 = x-3/-2

2(y-4) = 6(x-3)

y-4 = 3x-9

3x-y-5 = 0 is the eq of the line

» Find x intercept: y = 0

3x = 5

x = 5/3.... point (5/3,0) other (3,4) & (1,-2)

$r = \frac{ \sqrt{(x - x1) {}^{2} + (y - y1) {}^{2} } }{ \sqrt{(x - x2) {}^{2} + (y - y2) {}^{2} } }$

R = √(5/3-3)² + (0-4)² / √(5/3-1)² + (0+2)²

R = √16/9 + 16 / √ 4/9 + 4

R = 4√10/9 / 2√10/9

R = 4/2

R = 2/1

Ratio = 2:1