Question

the coordinates of the endpoints of \\( \overline { a b } \\) and \\( \overline { c d } \\) are \\( a ( 3,6 ) , b ( 8,7 ) , c ( 3,3 ) \\), and \\( d ( 8,4 ) \\). which statement describes how \\( \overline { a b } \\) and \\( \overline { c d } \\) are related?
\\( \bigcirc \\) a. \\( \overline { a b } \parallel \overline { c d } \\)
\\( \bigcirc \\) b. \\( \overline { a b } \perp \overline { c d } \\), and \\( \overline { a b } \\) bisects \\( \overline { c d } \\)
\\( \bigcirc \\) c. \\( \overline { a b } \perp \overline { c d } \\), but \\( \overline { a b } \\) does not bisect \\( \overline { c d } \\).
\\( \bigcirc \\) d. \\( \overline { a b } \\) is neither parallel nor perpendicular to \\( \overline { c d } \\)

Explanation:

Step1: Calculate the slope of \(\overline{AB}\)

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(3,6)\) and \(B(8,7)\), \(m_{AB}=\frac{7 - 6}{8 - 3}=\frac{1}{5}\)

Step2: Calculate the slope of \(\overline{CD}\)

For points \(C(3,3)\) and \(D(8,4)\), \(m_{CD}=\frac{4 - 3}{8 - 3}=\frac{1}{5}\)

Step3: Check if lines are parallel

Two lines are parallel if their slopes are equal. Since \(m_{AB}=m_{CD}=\frac{1}{5}\), \(\overline{AB}\parallel\overline{CD}\)

Answer:

A. \(\overline{AB}\parallel\overline{CD}\)