Segment Division

Question

In what ratio the segment joining the points (3,4) and (2,-3) is divided by the x-axis? Also, Find the ratio in which it is divided by the y-axis.

Answer 1

(3,4) and (2,-3) have a line joining them that has slope = (4+3)/(3-2) = 7

the equation of the line is y-4 = 7(x-3) = 7x -21

y= 7x -17 which has y intercept =-17

the y axis doesn't divide the line segment between the 2 given points

let y= 0 and solve for x to find the x intercept

0=7x-17

7x = 17

x= 17/7

x intercept = (17/7, 0) = (2 3/7, 0)

from (3,4) to (2 3/7, 0) = sqr(16/49+16)= (4/7)sqr50

from (2,-3) to (2 3/7, 0) =sqr(9/49+9)= (3/7)sqr50

(17/7,0) divides the line segment in a ratio of (3/7)sqr50:(4/7)sqr50 = 3:4