Prove that the points (– 4, – 1), (– 2, – 4), (4, 0) and (2, 3) are the vertices of a rectangle.

To Prove: Given vertices are of the rectangle.

Explanation: We have given points A(– 4, – 1), B(– 2, – 4), C(4, 0) and D(2, 3)

The points are joining in the form of 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_CD and m_{BC =} m_AD

i.e, AB CD and BC AD

And, m_AB×m_BC =

M_CD×m_AD =

So, that ABBC and CDAD

Hence, ABCD is a Rectangle.