Vertex points

Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.

Correct answer:

S =  84

Step-by-step explanation:

$$\begin{gathered} P_x=-12;P_y=6 \\ {Q}_x=4;Q_y=0 \\ {R}_x=-8;R_y=-6 \\ r=\sqrt{(P_x-Q_x{)}^2+(P_y-Q_y{)}^2}=\sqrt{((-12)-4{)}^2+(6-0{)}^2}=2\sqrt{73}\doteq 17.088 \\ p=\sqrt{(R_x-Q_x{)}^2+(R_y-Q_y{)}^2}=\sqrt{((-8)-4{)}^2+((-6)-0{)}^2}=6\sqrt{5}\doteq 13.4164 \\ q=\sqrt{(R_x-P_x{)}^2+(R_y-P_y{)}^2}=\sqrt{((-8)-(-12){)}^2+((-6)-6{)}^2}=4\sqrt{10}\doteq 12.6491 \\ s={\displaystyle \frac{r+p+q}{2}}={\displaystyle \frac{17.088+13.4164+12.6491}{2}}\doteq 21.5768 \\ S=\sqrt{s\cdot (s-r)\cdot (s-p)\cdot (s-q)}=\sqrt{21.5768\cdot (21.5768-17.088)\cdot (21.5768-13.4164)\cdot (21.5768-12.6491)}=84 \end{gathered}$$

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