Question

If M is the midpoint of PQ and X is the midpoint of PM then PX = a PQ Which statement is True? a is equal to 1 a is equal to 1/2 a is equal to 3/4 a is equal to 1/4

Answer 1

Answer:

D. a is equal to  $\frac{1}{4}$

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 $\frac{1}{4}$, so that;

PX = 8a

     = 8 x  $\frac{1}{4}$

     = 2 units

Thus, a is equal to  $\frac{1}{4}$ is the correct option.