# The points W(-2,-2), X(-6,2) , Y(2,5) and Z(6,1) are the vertices of parallelogram WXYZ. Find the length of the diagonal XZ

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To find the length of the diagonal XZ, you use the distance formula:

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

where d = length

You can consider any of the point X or point Z is point 1 or 2. Just be consistent. If x2 = 6 then y2 = 1.

Applying the formula, you have:

`d = sqrt((6-(-6))^2 + (1-2)^2)`

`d = sqrt((6+6)^2 + (-1)^2)`

`d = sqrt(145)`

Since it is not a perfect square and no factor of 145 is a perfect square, you can have `sqrt(145)` as the answer or you can use your calculator to get the decimal equivalent of 12.0416 units.

W(-2,-2),X(-6,2),Y(2,5) and Z(6,1)

We use distance formula to find the length of diagonal XZ.

`d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)`

`ZX=sqrt((-6-6)^2+(2-1)^2)`

`ZX=sqrt((-12)^2+1^2)`

`ZX=sqrt(144+1)`

`ZX=sqrt(145)`

`ZX=XZ`

Because length always taken as positive.