If R is the midpoint of QS, RS = 2 - 4, ST = 4r - 1, and RT = 8r - 43, find 0S.

Answer 1

Since R is the midpoint of QS, we have RS = ST. Therefore, we set the two given expressions for RS and ST equal to each other:

2 - 4 = 4r - 1

Next, we solve for r:

-2 = 4r - 1

-2 + 1 = 4r

-1 = 4r

r = -1/4

Now that we have the value of r, we can substitute it into the expression for RT:

RT = 8r - 43
= 8(-1/4) - 43
= -2 - 43
= -45

Therefore, OS = -45.