Answer:
D. a is equal to [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Let us assume that segment PQ is 8 units, so that its midpoint M is at 4 units to both P and Q.
Given that X is the midpoint of PM, this implies that X is at 2 units to both P and M.
Then;
PX = aPQ
⇒ = a x 8
= 8a
Therefore, a must be equal to [tex]\frac{1}{4}[/tex], so that;
PX = 8a
= 8 x [tex]\frac{1}{4}[/tex]
= 2 units
Thus, a is equal to [tex]\frac{1}{4}[/tex] is the correct option.
