Question

Show that the points A(-1.5,3) B(6,-2),C(-3,4) are collinear

Answer 1

if the vertices of points are equal to zero
they are said to be collinear

Answer 2

Answer:

Points are collinear as area of triangle is zero.

Step-by-step explanation:

Given : Points A(-1.5,3) B(6,-2),C(-3,4)

To find : Show that the points A(-1.5,3) B(6,-2),C(-3,4) are collinear?

Solution :

For A, B and C to be collinear, the area of triangle formed by them must be zero units.

Let $A(x_1,y_1)=(-1.5,3), B(x_2,y_2)=(6,-2),C(x_3,y_3)=(-3,4)$

Using Triangle Formula,

$A= \frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

$A= \frac{1}{2}[-1.5(-2-4)+6(4-3)-3(3+2)]$

$A= \frac{1}{2}[-1.5(-6)+6(1)-3(5)]$

$A= \frac{1}{2}[9+6-15]$

$A= 0$

Since, The area of triangle is zero.

Therefore, The points are collinear.