Question

Find the ratio in which the point (5+a/7,6a+3/7) divides the join of (1,3) and (2,7). Also find the value of a

Answer 1

Answer:

3:4

a = 5

Step-by-step explanation:

Find the ratio in which the point (5+a/7,6a+3/7) divides the join of (1,3) and (2,7). Also find the value of a

point (5+a/7,6a+3/7) lies on Line segment joing (1,3) and (2,7)

so slope must be same

Slope of Line =  (y2 - y1)/(x2 -x1)

= (7 - 3)/(2 - 1)

= 4/1

= 4

Slope   ((6a+3)/7 - 3)/( (5+a)/7 - 1)  = 4

=> (6a+3)/7  - 3  = 4(5+a)/7  - 4

=> 6a + 3 -21 = 20 + 4a -28

=> 2a = 10

=> a = 5

Point  ( 10/7 , 33/7)

if ratio is m :n

(2m + n)/(m+n)  ,  (7m + 3n)/(m + n)

=>( 2m + n)/(m + n) = 10/7

=> 14 m + 7n = 10m + 10n

=> 4m = 3n

=> m/n = 3/4

Ratio 3 : 4