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} ) is
the slope of ( overline{lm} ) is
the slope of ( overline{mn} ) is ( -\frac{1}{2} ). the slope of ( overline{kn} ) is 0. therefore,
because parallel segments have the same slope. by the
definition of a trapezoid, ( klmn ) is a trapezoid.

Explanation:

Step1: Calculate the slope of \(KL\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(K(0,0)\) and \(L(a,b)\), \(m_{KL}=\frac{b - 0}{a - 0}=\frac{b}{a}\).

Step2: Calculate the slope of \(LM\)

For points \(L(a,b)\) and \(M(3a,b)\), \(m_{LM}=\frac{b - b}{3a - a}=0\).

Step3: Determine the parallel sides

Since \(m_{KL}=\frac{b}{a}\), \(m_{LM} = 0\), \(m_{MN}=-\frac{1}{2}\), \(m_{KN}=0\). The sides \(KN\) and \(LM\) have the same slope (\(m = 0\)).

Answer:

The slope of \(\overline{KL}\) is \(\frac{b}{a}\). The slope of \(\overline{LM}\) is \(0\). The correct option for the parallel - sides statement is \(KN\) is parallel to side \(LM\).