Question

select the correct answer from each drop - down menu. given: k(0,0), l(a,b), m(3a,b), n(4a,0) are the vertices of quadrilateral klmn, where a ≠ 0 and b ≠ 0. prove: klmn is a trapezoid. k(0,0), l(a,b), m(3a,b), n(4a,0) are the vertices of quadrilateral klmn. the slope of each segment can be calculated. the slope of \\(\overline{kl}\\) is b/a. the slope of \\(\overline{lm}\\) is 0. the slope of \\(\overline{mn}\\) is -\\(\frac{b}{a}\\). the slope of \\(\overline{kn}\\) is 0. therefore drop - down menu with options: kl is parallel to side mn; kn is parallel to side lm; kl is parallel to side lm because parallel segments have the same slope. by the definition of a trapezoid, klmn is a trapezoid.

Explanation:

Step1: Recall slope formula

Slope between $(x_1,y_1)$ and $(x_2,y_2)$: $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Match equal slopes

Slope of $\overline{LM}=0$, slope of $\overline{KN}=0$. Parallel lines have equal slopes.

Answer:

KN is parallel to side LM