Find the coordinates of $P, Q, R$.

Question

In triangle $PQR$, $A(-2,3), B(5,-1)$ and $C(-4,-7)$ are the midpoints of $PQ, QR$ and $PR$ respectively. Find the coordinates of P, Q and R.

I really can't understand how to begin....Please hint :'(

Answer 1

$$x_{p}= x_{a} + x_{c}- x_{b}= -11$$ $$x_{q}= x_{a} + x_{b}- x_{c}= 7$$ $$x_{r}= x_{b} + x_{c}- x_{a}= 3$$

$$y_{p}= y_{a} + y_{c}- y_{b}= -3$$ $$y_{q}= y_{a} + y_{b}- y_{c}= 9$$ $$y_{r}= y_{b} + y_{c}- y_{a}= -11$$

P(-11,-3)

Q(7,9)

R(3,-11)

Answer 2

Hint: If we denote $P$ as $(x_{P},y_{P})$ and similarly for the other coordinates then since $A$ is the mid point of two of the sides of the triangle, say $P,Q$ then $$x_{A}=-2=\frac{x_{P}+x_{Q}}{2}$$ is the average of the $x$ values of the two sides.

Similarly $$y_{A}=3=\frac{y_{P}+y_{Q}}{2}$$

Write the other equations and solve for $x_A,y_A$ and for the $B,C$ values as well

Answer 3

$P=A+(C-B)$, $Q=A+(A-P)$ and $R=B+(B-Q)$.