Question

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

Explanation:

Step1: Calculate slope of \(JK\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For \(J(-3,2)\) and \(K(4,-1)\), \(m_{JK}=\frac{-1 - 2}{4-(-3)}=\frac{-3}{7}=-\frac{3}{7}\)

Step2: Calculate slope of \(LK\)

For \(L(2,-5)\) and \(K(4,-1)\), \(m_{LK}=\frac{-1-(-5)}{4 - 2}=\frac{4}{2}=2\)

Step3: Calculate slope of \(ML\)

For \(M(-5,-2)\) and \(L(2,-5)\), \(m_{ML}=\frac{-5-(-2)}{2-(-5)}=\frac{-3}{7}=-\frac{3}{7}\)

Step4: Calculate slope of \(MJ\)

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

Step5: Check if it is a parallelogram

A parallelogram has both pairs of opposite sides parallel. Since \(m_{JK}=m_{ML}=-\frac{3}{7}\) and \(m_{LK}=m_{MJ}=2\), both pairs of opposite sides are parallel.

Answer:

The slope of \(JK\) is \(-\frac{3}{7}\), the slope of \(LK\) is \(2\), the slope of \(ML\) is \(-\frac{3}{7}\), the slope of \(MJ\) is \(2\). Quadrilateral \(JKLM\) is a parallelogram because both pairs of opposite sides are parallel.