To Prove: Given points are of Parallelogram.

Explanation: Let us Assume that we have points, A (– 2, – 1), B(4, 0), C(3, 3) and D(– 3, 2), are joining the sides as AB, BC, CD, and AD.

The formula used: The slope of the line, m =

Now, The slope of Line AB, m_AB =

m_AB =

The slope of BC, m_BC =

m_{BC =}

Now, The slope of Line CD, m_CD =

m_CD =

The slope of AD, m_AD =

m_{AD =}

Here, We can see that, m_{AB =} m_CDand m_{BC =} m_AD

i.e, AB CD and BC AD

We know, If opposite side of a quadrilateral are parallel that it is parallelogram.

Hence, ABCD is a Parallelogram.