Question

In what ratio does the y-axis divide the line segment joining the points (-4,7)and (3,-7).Also find the coordinates of point of division.

Answer 1

Answer:

4 : 3 , (0, - 1)

Step-by-step explanation:

Slope m = ($y_{2}$ - $y_{1}$) / ($x_{2}$ - $x_{1}$)

m = $\frac{-7-7}{3-(-4)}$ = $\frac{-14}{7}$ = - 2

Let use point slope form formula (y - $y_{1}$) = m(x - $x_{1}$) to find the line passing through given points

y - 7 = - 2(x - (- 4))

y  - 7 = - 2x - 8

y = - 2x - 1 ===> y-intercept b = - 1  

y-axis divides the line segment AC in ratio AB : BC = 8 : 6 = 4 : 3

Coordinates of point of division are (0, - 1)  

Answer 2

Given  :  y-axis divide the line segment joining the points (-4,7)and (3,-7).

To find :  Ratio in which it divides &  coordinates of point of division.

Solution:

Y axis point =  ( 0  , a)

Let say it Divided points (-4,7)and (3,-7)  in ratio

k :  1

=>  (3k - 4)/(k + 1)  = 0    &  (-7k + 7)/(k + 1)  = a

=> 3k - 4 = 0                  

=> k = 4/3

=> 4 : 3 Ratio

a  =  (-7k + 7)/(k + 1)  

putting k = 4/3

=> a = (-7*4/3 + 7)/(4/3 + 1)

=> a = ( -28 + 21)/(4 + 3)

=> a = -7/7

=> a = - 1

Ratio in which it divides is 4 :3

coordinates of point of division. (0 , - 1)    

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