Question

Find the ratio in which line 3x+4y-9=0 divide the line segment joining the point (1,3),(2,7)

Answer 1

????????? yu thank yer formula is a line that hit differ line tween 2 points ??????

points: (1,3) & (2,7)

deltax=1, deltay=4, slope=4, angel=75.96 deg up from x-axis

midpoint=(1.5, 0.5)

line leng=4.123106

y=4x-1

###### other line: 3x+4y=9...or y=(9-3x)/4 or y=-0.75x +2.25

2 lines hit at (0.684211, 1.736844)

Answer 2

Let the line segment be divided in k:1 ratio

By Section Formulae =

X coordinate of point bisecting it = (1 + 2k)/(k+1)
Y coordinate of point bisecting it = (3 + 7k)/k+1)

By putting these values in the line

3x + y - 9 =0

we get
3((1 + 2k)/(k+1)) + (3 + 7k)/k+1) = 9
(3 + 6k)/k+1 + (3+7k)/(k + 1) = 9

6k+3+7k+3-9k-9=0

4k-3=0

k=3/4

k=3:4