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Answer:

A. 11

Step-by-step explanation:

-The diagonals of a Parallelogram  intersect each other at the midpoint.

-It therefore follows that:

[tex]XP=PZ\\\\PZ=0.5XZ[/tex]

#we equate and solve for X then determine the length of XP:

[tex]PZ=0.5XZ\\\\\therefore 4x-1=0.5(7x+1)\\\\4x-1=3.5x+0.5\\\\0.5x=1.5\\\\x=3\\\\PZ=4\times 3-1=11\\\\PZ=XP=11[/tex]

Hence, XP=11

In a parallelogram WXYZ.

The length of XP is 11.

The correct answer is option A.

WXYZ is a parallelogram

The diagonals of a parallelogram bisect each other: [tex]XZ=2PZ[/tex]

Substitute: [tex]XZ=7x+1, PZ=4x-1[/tex] into [tex]XZ=2PZ[/tex]

[tex]7x+1=2(4x-1)\\7x+1=8x-2\\x=3[/tex]

Segment Addition Postulate: [tex]XZ=XP+PZ[/tex]

[tex]7x+1=XP+4x-1\\XP=3x+2[/tex]

Put x = 3

[tex]XP=3(3)+2\\XP=11[/tex]

Therefore, The length of XP is 11.

For more information:

https://brainly.com/question/14632881

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