Question

1. look at the figure. find tw.

o 6
o 12
o 3
o 9

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(WY\) is perpendicular to \(TZ\) and \(Y\) is the mid - point of \(TZ\) (marked by the equal segments), by the perpendicular bisector theorem, \(TW = WZ\).

Step2: Set up the equation

We know that \(TW=x + 6\) and \(WZ = 3x\). So, \(x+6=3x\).

Step3: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(6=3x - x\), which simplifies to \(6 = 2x\). Then divide both sides by \(2\): \(x=\frac{6}{2}=3\).

Step4: Find the length of \(TW\)

Substitute \(x = 3\) into the expression for \(TW\). \(TW=x + 6\), so \(TW=3+6=9\).

Answer:

\(9\)