# Q is the midpoint of line segment PR. PQ=2z, and PR = 8z - 12. Please find z, PQ, and PR.

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PQ = 2z

PR = 8z - 12

But Q is midpoint of PR

Then,

PQ = (1/2)*PR

2z = (1/2)*(8z - 12)

2z = 4z - 6

==> 2z = 6

==>** z= 3**

**==> PQ = 2z = 2*3 = 6**

**==> PR = (8z - 12) = (8*3 - 12 = 24 - 12 = 12**

PR= 8Z - 12

if PQ is midpoint, then

PQ = 1/2 (PR)

2Z = 1/2 (8Z-12)

2Z= 4Z- 6

2Z=6

**Z=3**

PQ = 2Z

**PQ= 2*3=6**

PR= 8Z-12

PR= (8*3)-12

**PR= 24-12 = 12**

As Q is mid point of PR:

PQ = QR = PR/2

Given:

PR = 8z - 12

Therefore:

PQ = PR/2 = (8z - 12)/2 = 4z -6

As given:

PQ = 2z

Equating the given and above equated values of PQ:

2z = 4z - 6

==> 2z - 4z = - 6

==> -2z = - 6

==> z = -6/-2 = 3

Therefore:

PQ = 2z = 2*3 = 6

And:

PR = 2*PQ = 2*6 = 12

Answer:

z = 3

PQ = 6

PR= 12

Q is the midpoint of QR.

PQ = 2z and PR = PR = 8z-12.

To find PQ and PR.

Solution:

PQ = QR as Q is the mid point of PR by data.

2z = (1/2)(8z-12), as PQ= 2z and QR = (1/2)PR = (1/2)(8z-12) by data.

2z = 4z-6. Add 6 and subtract 2z

6 = 4z -2z

6 = 2z.

6/2 = z.

z = 3.

Therefore PQ = QR = 2z = 2*3 = 6

PR = 2*6 = 12.