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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)

Verified Answer :

MissPhiladelphia

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:

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)

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