Traingle again

Geometry Level 2

What is the area of the triangle $ABC$ with coordinates $A=(x,y), B=(2x,3y)$ and $C=(3x,5y)$ ?

where $x = \sqrt 2$ and $y = \pi$ .

1 solution

Ossama Ismail
Jan 29, 2016

The given 3 points are co-linear. Hence, it is a straight line.

Area of the triangle is 0.

Yes, they are collinear.But show it we can't say like this.

A Former Brilliant Member - 5 years, 4 months ago

Let the three points be $\displaystyle A(x, y)$ , $\displaystyle B(2x,3y)$ and $\displaystyle C(3x,5y)$ .

$\displaystyle Slope(BC) =\frac {5y-3y}{3x-2x} =\frac{2y}{x}$

$\displaystyle Slope(AB) =\frac{3y-y}{2x-x} =\frac{2y}{x}$

$\displaystyle \Rightarrow Slope(BC) =Slope(AB)$

$\displaystyle \Rightarrow A$ , $B$ and $C$ are collinear .

Harsh Khatri - 5 years, 4 months ago

It's not a triangle tho...

Brian Wang - 5 years, 4 months ago