if the points (- 2 ,1) (a,b) and (4 ,- 1) are collinear and a - b = 1 then find the values of a and b
No links

Question

if the points (- 2 ,1) (a,b) and (4 ,- 1) are collinear and a - b =
1 then find the values of a and b
No links

Rahul Gupta · Accepted Answer

Dear Student,
Let A-2,1; Ba,b; C4,-1 are the given points
Now, we know that if the points x1,y1;x2,y2 and x3,y3 are collinear, then 12x1y2-y3 + x2y3-y1 + x3y1-y2 = 0So, we have, x1=-2;y1 = 1 and x2 = a; y2  = b and x3 = 4;y3 = -1Now,   12-2b+1 + a-1-1 + 41-b = 0⇒-2b-2-2a+4-4b = 0⇒-2a-6b+2 = 0⇒2a+6b-2 = 0⇒a+3b-1 = 0⇒a + 3b = 1       
1Also, a - b = 1    
2Subtracting 2 from 1, we get    4b = 0⇒b = 0Now, from 2, we get a = 1So, a = 1; b = 0
Regards

if the points (- 2 ,1) (a,b) and (4 ,- 1) are collinear and a - b = 1 then find the values of a and b No links

if the points (- 2 ,1) (a,b) and (4 ,- 1) are collinear and a - b = 1 then find the values of a and b
No links