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

The coordinates are (-r,0)

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}`

`((x_1+x_2)/(2),(y_1+y_2)/(2))`

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

`((-p-r)/(2),(q)/(2))`

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

`((-p+x)/(2),(q+y)/(2))`

As the diagonals of parallelogram bisect each other.

`((-p-r)/(2),(q)/(2))=((-p+x)/(2),(q+y)/(2))`

Comparing, we get

`(-p+x)/(2)=(-p-r)/(2)`

`x=-r`

`(q)/(2)=(q+y)/(2)`

`y=0`

Hence, the coordinates are (-r,0)

Answer 2

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.