17. Five mark exercise problem IV

Let $P(11,7)$, $Q(13.5,4)$ and $R(9.5,4)$ be the midpoints of the sides $AB$, $BC$ and $AC$ respectively of $\triangle ABC$. Find the coordinates of the vertices $A$, $B$ and $C$. Hence find the area of $\triangle ABC$ and compare this with area of $\triangle PQR$.

 

Answer:

 

Coordinates of $A =$ $\left(i,i\right)$

 

Coordinates of $B =$ $\left(i,i\right)$

 

Coordinates of $C =$ $\left(i,i\right)$

 

Area of $\triangle ABC =$

 

Area of $\triangle PQR =$

 

Area of $\triangle ABC =$  $\times$ Area of $\triangle PQR$.