Question

plot the following point and Check whether they are collinear or not(-1,1),(-3,3),(-5,5)

Answer 1

yes they are collinear

Answer 2

Given,

Coordinates of the given points are = (-1,1) , (-3,3) , (-5,5)

To find,

The given points are collinear or not.

Solution,

We can easily find out that the given points are either collinear or not. We have to calculate the area of the triangle formed by the given points, and if the value of the area of the triangle becomes zero, then we can confirm that the given points are collinear.

Point A = (-1,1) = X1,Y1

Point B = (-3,3) = X2,Y2

Point C = (-5,5) = X3,Y3

Now, we have to calculate the area of the ∆ABC by using the following mathematical formula.

Area of ∆ABC :

= ½ {X1(Y2-Y3) + X2(Y3-Y1) + X3(Y1-Y2)}

= ½ {(-1) (3-5) + (-3) (5-1) + (-5) (1-3)}

= ½ (2-12+10)

= ½ (-10+10)

= ½ × 0

= 0

Area of ∆ABC is zero, so the three points are collinear and the graph plotting diagram is attached below.

Hence, A,B,C are collinear points.