Question

Determine if the points (2,3),(4,0) and (6,-3) are collinear

Answer 1

if a straight line will be there then these ae collinear points

means if u will plot the points on graph and after plotting and joining them together if you get get straight line then those points are collinear

Answer 2

for proving a point collinear we need to prove that the area of triangle formed by the 3 points is zero i.e. no triangle is formed..
points are (2,3)(4,0)(6,-3)
x1=2 x2=4 x3=6
y1=3 y2=0 y3=-3
so area of triangle
0=½[x1(y2-y3) +x2(y3-y1)+x3(y1-y2)
0=[2(0+3)+4(-3-3)+6(3-0)]
0=[6-24+18]
0=0
hence the points are collinear