Question

points n, k, and p are collinear. n is between k and p. kp = 29, pn = 2x + 14, and kn = 3x - 1. is n the midpoint of kp? o no, n is the midpoint of kp because pn = 16 and kn = 17 o yes, n is the midpoint of kp because pn = 14 and kn = 14 o no, n is the midpoint of kp because pn = 8 and kn = 5 o yes, n is the midpoint of kp because pn = 6 and kn = 6

Explanation:

Step1: Recall mid - point property

If N is the mid - point of KP, then PN = KN.

Step2: Check given lengths

Given PN = 2x + 4 and KN = 3x - 1. Set PN = KN:
2x + 4=3x - 1.

Step3: Solve for x

Subtract 2x from both sides: 4=x - 1. Then add 1 to both sides, we get x = 5.

Step4: Find lengths of PN and KN

Substitute x = 5 into PN = 2x+4, PN=2×5 + 4=14. Substitute x = 5 into KN = 3x - 1, KN=3×5 - 1=14.
Since PN = KN = 14, N is the mid - point of KP.

Answer:

Yes, N is the mid - point of KP because PN = 14 and KN = 14.