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 intersection

Answer 1

Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the ratio k: 1. Using section formula, we have: Thus, the required co-ordinates of the point of intersection are (10/3,0)

Answer 2

Answer:

divided in the ratio 2:5 and point of intersection = (26/7 , 0)

Step-by-step explanation:

Given , A (4,2) and B (3,-5)

Therefore ,

x1=4

y1=2

x2=3

y2=-5

Let point of intersection be P (x,y)

we know P is on x-axis , therefore P = (x,0)

Let the ratio in which it is divided be m1:m2

0= (m1y2+m2y1)/(m1+m2)

Transposing (m1+m2)

we get ,

0= m1y2+m2y1

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

5m1= 2 m2

=> m1/m2= 2/5

therefore ratio = m1:m2= 2:5

now , using this to find x-co-ordinate of P

x= (m1x2+m2x1)/(m1+m2)

x= ( (2 x 3) + (5 x4)) / (2+5)

x= (6+20)/7

x= 26/7

Therefore P (x,0)= (26/7 , 0)

and ratio in which AB is divided is 2:5.

The End.