Question

select the correct answer.
quad is a quadrilateral with vertices ( q(-3,2) ). ( u(3,0) ). ( a(6,-5) ). and ( d(0,-3) ). the slope for ( overline{qu} ) is ( \frac{0 - 2}{3 - (-3)} = -\frac{1}{3} ). the slope for ( overline{ua} ) is ( \frac{-5 - 0}{6 - 3} = -\frac{5}{3} ).
the slope for ( overline{ad} ) is ( \frac{-3 - (-5)}{0 - 6} = -\frac{1}{3} ). the slope for ( overline{dq} ) is ( \frac{-3 - 2}{0 - (-3)} = -\frac{5}{3} ). so. ______. therefore, quad is a parallelogram.
what is the missing step in the proof?
( \bigcirc ) a. ( overline{qu} perp overline{ad} ) and ( overline{ua} perp overline{dq} ) because the segments have the same slope.
( \bigcirc ) b. ( overline{qu} parallel overline{ad} ) and ( overline{ua} parallel overline{dq} ) because the product of the slopes is -1.
( \bigcirc ) c. ( overline{qu} perp overline{ad} ) and ( overline{ua} perp overline{dq} ) because the product of the slopes is -1.
( \bigcirc ) d. ( overline{qu} parallel overline{ad} ) and ( overline{ua} parallel overline{dq} ) because the segments have the same slope.

Explanation:

Step1: Recall the property of parallel lines

If two lines are parallel, their slopes are equal.

Step2: Analyze the slopes

Slope of \(\overline{QU}\) is \(-\frac{1}{3}\), slope of \(\overline{AD}\) is \(-\frac{1}{3}\). So \(\overline{QU}\parallel\overline{AD}\).
Slope of \(\overline{UA}\) is \(-\frac{5}{3}\), slope of \(\overline{DQ}\) is \(-\frac{5}{3}\). So \(\overline{UA}\parallel\overline{DQ}\).

Answer:

D. \(\overline{QU}\parallel\overline{AD}\) and \(\overline{UA}\parallel\overline{DQ}\) because the segments have the same slope.