Question

the coordinates of the vertices of quadrilateral ( jklm ) are ( j(-4,1) ), ( k(2,3) ), ( l(5,-3) ), and ( m(0,-5) ).
drag and drop the choices into each box to correctly complete the sentences.
the slope for ( overline{jk} ) is
, the slope of ( overline{lk} ) is
, the slope of ( overline{ml} ) is
, and the slope of ( overline{mj} ) is
. quadrilateral ( jklm )
a
parallelogram because
.

Explanation:

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For points \(J(-4,1)\) and \(K(2,3)\), \(m_{JK}=\frac{3 - 1}{2-(-4)}=\frac{2}{6}=\frac{1}{3}\)

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

For points \(L(5,-3)\) and \(K(2,3)\), \(m_{LK}=\frac{3-(-3)}{2 - 5}=\frac{6}{-3}=- 2\)

Step3: Calculate the slope of \(\overline{ML}\)

For points \(M(0,-5)\) and \(L(5,-3)\), \(m_{ML}=\frac{-3-(-5)}{5 - 0}=\frac{2}{5}\)

Step4: Calculate the slope of \(\overline{MJ}\)

For points \(M(0,-5)\) and \(J(-4,1)\), \(m_{MJ}=\frac{1-(-5)}{-4-0}=\frac{6}{-4}=-\frac{3}{2}\)

Step5: Check if it is a parallelogram

A parallelogram has opposite sides parallel (equal slopes). Here, \(m_{JK}
eq m_{ML}\) and \(m_{LK}
eq m_{MJ}\)

Answer:

The slope of \(\overline{JK}\) is \(\frac{1}{3}\), the slope of \(\overline{LK}\) is \(-2\), the slope of \(\overline{ML}\) is \(\frac{2}{5}\), the slope of \(\overline{MJ}\) is \(-\frac{3}{2}\). Quadrilateral \(JKLM\) is not a parallelogram because opposite sides do not have equal slopes.