Question

what is the probability that a random point on (overline{ab}) will be on (overline{cd})?

Explanation:

Step1: Calculate the length of CD

The length of a line segment with endpoints \(x_1\) and \(x_2\) is \(|x_2 - x_1|\). For \(\overline{CD}\), \(x_1 = 51\) and \(x_2=60\). So, \(CD=|60 - 51|=9\).

Step2: Calculate the length of AB

For \(\overline{AB}\), \(x_1 = 48\) and \(x_2 = 68\). So, \(AB=|68 - 48|=20\).

Step3: Calculate the probability

The probability \(P\) that a random point on \(\overline{AB}\) is on \(\overline{CD}\) is given by the formula \(P=\frac{\text{length of }CD}{\text{length of }AB}\). Substituting the values, \(P=\frac{9}{20}=0.45\).

Answer:

\(0.45\)