Question

HELP ASAP 30 POINTS GIVEN

The coordinates of the vertices of  quadrilateral JKLM are J(−3, 2), K(4, −1), L(2, −5), and(−5, −2). Drag and drop the choices into each box to correctly complete the sentences.

Answer 1

The slope of JK is -3/7
The slope of LK is 2
The slope of ML is -3/7
The slope of MJ is 2
Quadrilateral JKLM is a parallelogram because both pairs of opposite sides are parallel. YOU'RE WELCOME :D

Answer 2

`-(3)/(7)`,
`2`,
`-(3)/(7)`,
`2`,is,both pairs of opposite sides are parallel

Explanation:

Given two points

`A=(a1,a2)` and

`B=(b1,b2)`

We define the slope ''m'' between this points as :

`m=(b2-a2)/(b1-a1)` or either

`m=(a2-b2)/(a1-b1)`

The slope between the points J and K is

`m=(-1-2)/(4-(-3))=-(3)/(7)`

The slope between the points L and K is

`m=(-1-(-5))/(4-2)=2`

The slope between the points M and L is

`m=(-2-(-5))/(-5-2)=-(3)/(7)`

The slope between the points M and J is

`m=(-2-2)/(-5-(-3))=2`

We find all the slopes between the points.

For the quadrilateral JKLM the side JK is opposite to the side ML and the side KL is opposite to the side JM

The definition of parallelogram is :

A figure with 4 sides in which their opposite sides are parallel.

The side JK is parallel to the side ML because they have the same slope.

The side JM is parallel to the side KL because they have the same slope.

We answer that JKLM is a parallelogram because both pairs of opposite sides are parallel.