Question

Calculate the area of a triangle with vertices $\left(1,1\right)$,$\left(3,1\right)$ And $\left(5,7\right)$ .

Answer 1

Calculate the area of a triangle:

Given vertices of a triangle are $\left(1,1\right)$,$\left(3,1\right)$ And $\left(5,7\right)$ .

So, we have

$x_1=1,y_1=1$

$x_2=3,y_2=1$

$x_3=5,y_3=7$

By the formula of area of triangle when coordinates of vertices are given, we have;

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;

$$\begin{gathered} =\frac{1}{2}\left[1\left(1-7\right)+3\left(7-1\right)+5\left(1-1\right)\right] \\ =\frac{1}{2}\left[1\left(-6\right)+3\left(6\right)+5\left(0\right)\right] \\ =\frac{1}{2}\left[-6+18+0\right] \\ =\frac{1}{2}\left[12\right] \\ =\frac{1}{2}\times 12 \\ =6sq.unit \end{gathered}$$

Therefore, the area of a triangle formed from the given points is $6$ square units.