Question

if (1,a),(3,9a),(4,b),(6,18) are collinear,then (a,b/a)=

Answer 1

If these four points are "collinear" then slope of the line connecting any two points would be same as that of the line connecting any two.
So,taking the first two points:
Slope=(9a-a)/(3-1) = 4a.
Now taking the first and last point:
Slope=(18-a)/(6-1) = (18-a)/5.
Equating both of them:
(18-a)/5 =4a which implies 18=21a
Which means that a=7/6.
Now taking the third and fourth points:
Slope=(18-b)/(6-4)= (18-b)/2 which is equal to 4a = 28/6 = 14/3
(18-b)/2 =14/3 which implies 28=54-3b
Which means that b=26/3.

Answer 2

Answer:

The value of (a, b/a ) = (6/7 , 13)

Step-by-step explanation:

• Three or more points are said to be collinear if the slope of any two pairs of points is the same.
• Slope of the line segment joining two points say (x1, y1) and (x2, y2) is given by the formula:
• m = (y2 – y1)/ (x2 – x1)
• Let point x(1,a) , y (3,9a), z (4,b) and w (6,18)
• The slope of the line joining x and y is m1 = (9a- a )/(3-1) = 8a/ 2 = 4a.............(i)
• The slope of the line joining x and w is m2 = (18-a)/(6-1) = (18-a)/5...............(ii)
• from (i) and (ii) we can write

(18-a)/5 = 4a

18 - a = 20a

21a = 18

a= 6/7

• The slope of the line joining z and w is

m3= (18-b)/(6-4) = (18-b) / 2 ..........(iii)

• Now, (18-b)/2 = 4a=4×(6/7) = 24/7

b= 78/7

Hence the value of (a, b/a ) = (6/7 , 13)