Question

The area of the triangle formed from points $(1,2),(2,4)$ and $(3,1)$ is ____ square units.

• A. $\frac{5}{2}$
• B. $\frac{2}{5}$
• C. $\frac{3}{2}$
• D. $2$

Answer 1

The correct option is A $\frac{5}{2}$

Formula for area of triangle is $\left|\frac{1}{2}\right[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\left]\right|$
where $x_1=1$, $y_1=2$, $x_2=2$, $y_2=4$, $x_3=3$ and $y_3=1$
Substitute the values, we get,
Area of triangle $=$ $|\frac{1}{2}\times [1(4-1)+2(1-2)+3(2-4)\left]\right|$
$=$ $|\frac{1}{2}\times [3-2-6\left]\right|$
$=$ $|\frac{1}{2}\times -5|$
$=$ $|-\frac{5}{2}|$
Area always in absolute value.
So, area of the triangle $=\frac{5}{2}$ square units.