Question

If the points A (-3,9) ,B(a,b), (4,-5) are collinear then prove that a+b= 1

Answer 1

Answer:

Given that,

A(-3,9), B(a,b), C(4,-5)

if the points are collinear, then area of triangle is equal to zero.

Area of ∆ABC=1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

0=1/2|-3(b+5)+a(-5-9)+4(9-b)|

0×2=|-3b-15+a(-14)+36-4b|

0=|-7b+21-14a|

-7b+21-14a=0

7(-b+3-2a)=0

-b+3-2a=0/7

-b+3-2a=0

-2a-b=-3

2a+b=3