Question

The points A(1,2), B(-2,1) and C(1,4) are
I) Collinear
ii) Non-collinear
iii) Form a triangle
iv)None of the above​

Answer 1

$\pmb {Answer:-}$

Option -B

$\pmb {Given:-}$

The points A (1, 2) B (-2 , 1) C (1, 4) are in

• Collinear
• Non - collinear
• Form a triangle
• None of the above

$\pmb{Solution:-}$

Firstly we find the area of those points by using Area of triangle formula.

If the Area is 0 then the given points are collinear and forms a triangle or quadrilateral . Here there are three points So, if its area is zero then it may form a triangle

If the Area is not 0 then the given points are non-collinear .

$\pmb {Area\: of \: triangle = \cfrac{1}{2} \bigg|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigg| }$

Substituting the values ,

$x_1 = 1 \\y_1 = 2 \\x_2 = -2 \\y_2 = 1\\x_3 = 1\\y_3 = 4$

$= \dfrac{1}{2} \bigg|1(1-4) -2(4-2)+1(2-1)\bigg|$

$= \dfrac{1}{2} \bigg|1(-3) -2(2)+1(1)\bigg|$

$= \dfrac{1}{2} \bigg|-3 -4+1\bigg|$

$= \dfrac{1}{2} \bigg|-7+1\bigg|$

$= \dfrac{1}{2} \bigg|-6\bigg|$

$=\cfrac{1}{2} (6)$

$=\dfrac{6}{2}$

$= 3sq.units$

Since area is not equal to 0 i.e the given points are non - collinear

So, the answer is Option -B