Question

show that the point (5,1),(1,-1) and (11,4) lie on the straight line

Answer 1

Given,

The points are (5,1),(1,-1) and (11,4).

To find,

The given points are colinear.

Solution,

If the given points are colinear then the area of the triangle made by these three points will be zero. We will be assume that these three points are three vertices of an imaginary triangle to find wether the area of the triangle is zero or not. If the calculated area becomes zero then we can say that the given points are colinear.

Let,

x1,y1 = 5,1

x2,y2 = 1,-1

x3,y3 = 11,4

So,the area of the triangle

= [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)]

= [5(-1-4) + 1(4-1) + 11(1+1)]

= [-25 + 3 + 22]

= 0

Hence,the given three points lie on the straight line.