Question

show that points A(-4,-7) ,B(-1,2),C(8,5)and D(5,-4) are the vertices of rhombus ABCD

Answer 1

Step-by-step explanation:

slope of line AB=y2-y1/x2-x1

=2-(-7)/-1-(-4)

=9/3

=3

slop of linr CD=same formula

=-4-(-5)/5-8

=9/3

=3

therefore,slope of line AB=slope of lineCD

hence,ABCD is a rhombus.

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Answer 2

Step-by-step explanation:

Slope of Line AB = y2 - y1 / x2 - x1

                            = 2 - (-7) / -1 -( -4)

                        = 9 / 3  =  3

Slope of Line BC = y2 - y1 / x2 - x1

                            = 5 - 2 / 8 - (-1)

                        = 3 / 9  =  1/3

Slope of Line CD = y2 - y1 / x2 - x1

                             = - 4 - 5 / 5 - 8

                         = - 9 / - 3  =  3

Slope of Line AD = y2 - y1 / x2 - x1

                            = -4 - (- 7) / 5 - (- 4)

                        = 3 / 9  =  1/3

AB = CD = 3

BC = AD = 1/3

So, these are the vertices of parallelogram ABCD.