Question

r is the midpoint of $overline{qs}$. if $qr = x + 5$ and $rs = 4x - 10$, what is $rs?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(R\) is the mid - point of \(\overline{QS}\), then \(QR = RS\). So we set up the equation \(x + 5=4x-10\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(5 = 4x-x-10\), which simplifies to \(5 = 3x-10\). Then add 10 to both sides: \(5 + 10=3x\), so \(15 = 3x\). Divide both sides by 3, we get \(x = 5\).

Step3: Find \(RS\)

Substitute \(x = 5\) into the expression for \(RS\). Since \(RS=4x - 10\), then \(RS=4\times5-10\).
\(RS=20 - 10=10\).

Answer:

10