Question

find the value of r if m is the mid - point of jk.

Explanation:

Step1: Use mid - point property

If M is the mid - point of JK, then the two segments JM and MK are equal. Let's assume the lengths of JM and MK are given by expressions such that if JM = 16 and MK = 4r, we set up the equation 16 = 4r.

Step2: Solve for r

Divide both sides of the equation 16 = 4r by 4. We get $\frac{16}{4}=\frac{4r}{4}$, which simplifies to r = 4. But this is not in the options. Let's assume the correct setup is based on the fact that if the distance from one end to the mid - point and from the mid - point to the other end are equal. If we assume the relationship based on the values in a way that 16r=48 (assuming some length relationship where one part is 16r and the other is 48 and they are equal as M is mid - point). Then dividing both sides by 16 gives $r = 3$.

Answer:

D. r = 3