Question

The coordinates of parallelogram PVWZ are P(0, 0), V(-p, q), and W(-p - r, q). Find the coordinates of Z without using any new variables.
(0, -r)

(p + r, q)

(-r, 0)

(-p, -q)

Answer 1

For the answer to the question above asking to find the coordinates of Z without using any new variables. 


Vector WZ equals vector VP, which is (p, -q) 
So Z is (-p - r + p, q - q) which is (-r, 0)
I hope my answer helped you. 

Answer 2

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 $(x_1,y_1)\text{ and }(x_2,y_2) \text{ are the coordinates of line segment the coordinates of mid-point are}$

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Mid-point of line segment joining the line P(0,0) and W(-p-r, q).

$(\frac{-p-r}{2},\frac{q}{2})$

Mid-point of line segment joining the line V(-p, q) and Z(x,y)

$(\frac{-p+x}{2},\frac{q+y}{2})$

As the diagonals of parallelogram bisect each other.

$(\frac{-p-r}{2},\frac{q}{2})=(\frac{-p+x}{2},\frac{q+y}{2})$

Comparing, we get

$\frac{-p+x}{2}=\frac{-p-r}{2}$

$x=-r$

$\frac{q}{2}=\frac{q+y}{2}$

$y=0$

Hence, the coordinates are (-r,0)