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

Answer 1

Since R is the midpoint of segment QS, we know that RS = ST. Setting these two expressions equal to each other, we get:

2x - 4 = 4x - 1

Subtracting 2x from both sides, we have:

-4 = 2x - 1

Adding 1 to both sides:

-3 = 2x

Dividing both sides by 2:

x = -3/2

Now we can substitute this value of x back into any of the original expressions to find the lengths of the segments. Let's use RS = 2x - 4:

RS = 2(-3/2) - 4

RS = -3 - 4

RS = -7

Since RS represents half of the length of segment QS, we can multiply -7 by 2 to find QS:

QS = 2 * (-7)
QS = -14

Therefore, the length of segment QS is -14.