Question

In what ratio is the line joining the points (4, 2) and (3, -5) divided by the x-axis? Also, find the coordinates of the point of
division

Answer 1

given divided by x axis

therefore y=0

given, x1=4, y1=2 and x2=3, y2= -5.

y= m1y2+ m2y1 /m1+m2

as, y =0

0=m1× -5 + m2× 2/ m1+m2

0(m1+m2) = -5m1+2m2

0= -5m1 + 2 m2

5m1=2m2

m1/m2=2/5

m1:m2=2:5 (m1=2, m2=5)

therefore the ratio is,

2:5

p(x, y)

=(m1x2+m2x1) /m1+m2 (m1y2+m2y1) /m1+m2

=(2×3 + 5×4) /2+5 ,( 2×-5+ 5×2) / 2+5

= (6+20) /7 , (-10+10) /7

= 26/ 7, 0/7

=3.7, 0