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 \(\triangle PQR\).