Question

Do the points (5,6),(4,5),(3,4) lie on a straight line? ​

Answer 1

we can tell it by using the area of triangle formula

if we assume that they are vertices of a triangle then the area of them should be some integral value if it is equal to 0 then they are in straight line

area of triangle = 1/2 | X1(y2-y3) + X2 ( y3- y1) + X3( y1- y2)|

Answer 2

We use the area of a triangle formula to calculate whether three points are on same line or not .
We than substitute the values and solve

* formula and method given in attachment*

Since the area is 0.

Therefore, the three points are collinear.

i.e. they lie in a straight line.