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
eq0 ) and ( b
eq0 ).
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} ) (dots) the slope of ( overline{lm} ) is (dots)
the slope of ( overline{mn} ) (dots) the slope of ( overline{kn} ) is 0. therefore, (dots) because parallel segments have the same slope. by the definition of a trapezoid, ( klmn ) is a trapezoid.
(the drop - down options for slope include 0, ( -\frac{b}{a} ), undefined, ( \frac{b}{a} ))

Explanation:

Step1: Calculate slope of $\overline{KL}$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
For $K(0,0), L(a,b)$:
$m_{\overline{KL}}=\frac{b-0}{a-0}=\frac{b}{a}$

Step2: Calculate slope of $\overline{LM}$

For $L(a,b), M(3a,b)$:
$m_{\overline{LM}}=\frac{b-b}{3a-a}=\frac{0}{2a}=0$

Step3: Calculate slope of $\overline{MN}$

For $M(3a,b), N(4a,0)$:
$m_{\overline{MN}}=\frac{0-b}{4a-3a}=\frac{-b}{a}$

Step4: Identify parallel segments

Slope of $\overline{LM}=0$, slope of $\overline{KN}=0$. So $\overline{LM} \parallel \overline{KN}$

Answer:

1. Slope of $\overline{KL}$: $\boldsymbol{\frac{b}{a}}$
2. Slope of $\overline{LM}$: $\boldsymbol{0}$
3. Slope of $\overline{MN}$: $\boldsymbol{-\frac{b}{a}}$
4. Final blank: $\boldsymbol{\overline{LM} \text{ is parallel to } \overline{KN}}$