Notes: Please answer this question for I have a test coming up. My question is: Q. Given that the points (1,-1), (2,2) and (4,t) are collinear, find the...

Thursday, June 5, 2014

Please answer this question for I have a test coming up. My question is: Q. Given that the points (1,-1), (2,2) and (4,t) are collinear, find the...

If three points are collinear the area of the triangle formed by them is 0.

The formula to find area of a triangle formed by three points is

$\displaystyle\frac{{1}}{{2}}{\left[{x}_{{1}}{\left({y}_{{2}}-{y}_{{3}}\right)}+{x}_{{2}}{\left({y}_{{3}}-{y}_{{1}}\right)}+{x}_{{3}}{\left({y}_{{1}}-{y}_{{2}}\right)}\right]}$

Now the given points $\displaystyle{\left({1},-{1}\right)},{\left({2},{2}\right)}$ and $\displaystyle{\left({4},{t}\right)}$ are colliner. So the area is 0

Lets take these points as $\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)},{\left({x}_{{2}},{y}_{{2}}\right)},{\left({x}_{{3}},{y}_{{3}}\right)}$ and substitute in the formula