Question

14
given parallelogram defg, if df = 5x + 1, what is pf?
(there is a diagram of parallelogram defg with diagonals intersecting at point p. one segment from p to e is labeled 2x, and from p to g is labeled 3x - 5)
show your work here
○ 10
○ 13
○ 20
○ 26

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, diagonals bisect each other. So, \(PF = PD\). From the diagram, \(PF = 2x\) and \(PD = 3x - 5\), so \(2x=3x - 5\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(0=x - 5\). Then add 5 to both sides: \(x = 5\).

Step3: Find \(DF\)

Substitute \(x = 5\) into \(DF=5x + 1\): \(DF=5(5)+1=25 + 1=26\).

Step4: Find \(PF\)

Since diagonals bisect each other, \(PF=\frac{DF}{2}\). So \(PF=\frac{26}{2}=13\).

Answer:

13