Question

The area of the triangle whose vertices are $(0,1),(1,4)$ and $(1,2)$ is ___ square units.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

1

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 $x_1=0$, $y_1=1$, $x_2=1$, $y_2=4$, $x_3=1$ and $y_3=2$
Substitute the values, we get
Area of triangle $=$ $|\frac{1}{2}\times [0(4-2)+1(2-1)+1(1-4)\left]\right|$
$=$ $|\frac{1}{2}\times [0+1-3\left]\right|$
$=$ $|\frac{1}{2}\times -2|$
$=$ $|-1|$
Area always in absolute value.
So, area of the triangle is $1$ square units.