Final answer:
The value of R is found to be 6 by averaging the endpoints of segment PR, with P at -24 and Q at -9 as the midpoint. The correct answer is not among the given options.
Step-by-step explanation:
The question asks us to find the value of point R if Q is the midpoint of PR, and the values of P and Q are given as -24 and -9, respectively.
To find R, recall that the midpoint Q of a segment PR will be the average of the endpoints P and R. This is found using the formula:
Q = ( P + R ) / 2
Substituting the given values into the formula gives:
-9 = ( -24 + R ) / 2
We can then solve for R by multiplying both sides of the equation by 2 and adding 24 to both sides:
-18 = -24 + R
R = -18 + 24
R = 6
Thus, the correct value for R is not listed in the provided options (a) through (d).