Question

1. given c(x, 16), d(2, -4), e(-6, 14), and f(-2, 4), find the value of x so that \\(\overline{cd} \parallel \overline{ef}\\).

Explanation:

Step1: Find slope of \( \overline{EF} \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For \( E(-6, 14) \) and \( F(-2, 4) \), \( m_{EF} = \frac{4 - 14}{-2 - (-6)} = \frac{-10}{4} = -\frac{5}{2} \).

Step2: Find slope of \( \overline{CD} \)

For \( C(x, 16) \) and \( D(2, -4) \), \( m_{CD} = \frac{-4 - 16}{2 - x} = \frac{-20}{2 - x} \).

Step3: Set slopes equal (parallel lines)

Since \( \overline{CD} \parallel \overline{EF} \), \( m_{CD} = m_{EF} \). So \( \frac{-20}{2 - x} = -\frac{5}{2} \). Cross - multiply: \( -20\times2 = -5\times(2 - x) \).

Step4: Solve for \( x \)

Simplify: \( -40 = -10 + 5x \). Add 10 to both sides: \( -30 = 5x \). Divide by 5: \( x = -6 \).

Answer:

\( x = -6 \)