Question

Calculate the Area Of a Triangle Formed By The Points $A\left(5,2\right)$,$B\left(4,7\right)$ And $C\left(7,-4\right)$ .

Answer 1

Step:Calculate the Area Of a Triangle.

Given vertices of a triangle are $A\left(5,2\right)$,$B\left(4,7\right)$ And $C\left(7,-4\right)$ .

So, we have

$x_1=5,y_1=2$

$x_2=4,y_2=7$

$x_3=7,y_3=-4$

As we know the formula of Area Of a Triangle $=\frac{1}{2}\left[x_1\left\{y_2-y_3\right\}+x_2\left\{y_3-y_1\right\}+x_3\left\{y_1-y_2\right\}\right]$

Now by substituting the given coordinates, we get;

$$\begin{gathered} =\frac{1}{2}\left[5\left(7+4\right)+4\left(-4-2\right)+7\left(2-7\right)\right] \\ =\frac{1}{2}\left[5\left(11\right)+4\left(-6\right)+7\left(-5\right)\right] \\ =\frac{1}{2}\left[55-24-35\right] \\ =\frac{1}{2}\left[-4\right] \\ =\frac{1}{2}\times -4 \\ =-2 \end{gathered}$$

Therefore, the area of a triangle formed from the given points is $-2$ square units.