Answer:
The coordinates are (-r,0)
Step-by-step explanation:
Given the coordinates of parallelogram PVWZ are P(0,0), V(-p,q), and W(-p-r, q). we have to find the coordinates of Z.
Let coordinates of Z(x,y)
As the diagonals of parallelogram bisect each other.
Therefore, by using mid-point formula
If [tex](x_1,y_1)\text{ and }(x_2,y_2) \text{ are the coordinates of line segment the coordinates of mid-point are}[/tex]
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Mid-point of line segment joining the line P(0,0) and W(-p-r, q).
[tex](\frac{-p-r}{2},\frac{q}{2})[/tex]
Mid-point of line segment joining the line V(-p, q) and Z(x,y)
[tex](\frac{-p+x}{2},\frac{q+y}{2})[/tex]
As the diagonals of parallelogram bisect each other.
[tex](\frac{-p-r}{2},\frac{q}{2})=(\frac{-p+x}{2},\frac{q+y}{2})[/tex]
Comparing, we get
[tex]\frac{-p+x}{2}=\frac{-p-r}{2}[/tex]
[tex]x=-r[/tex]
[tex]\frac{q}{2}=\frac{q+y}{2}[/tex]
[tex]y=0[/tex]
Hence, the coordinates are (-r,0)
