Which statement explains the relationship of sides BA and B'A' after rectangle BADC has been rotated 90° clockwise about the origin?

coordinate plane with rectangle ABCD at A 3 comma 5, B 1 comma 3, C 5 comma negative 1, and D 7 comma 1

Side B'A' has a slope of −1 and is perpendicular to side BA.
Side B'A' has a slope of 1 and is parallel to side BA.
Side B'A' has a slope of 1 and is perpendicular to side BA.
Side B'A' has a slope of −1 and is parallel to side BA.

Side B'A has a slope of 1 and is perpendicular to side BA

Step-by-step explanation:

When rotating clockwise 90 degrees x,y will become y,-x so lets apply this to the points.

A=(3,5) -->(5,-3)

B=(1,3)-->(3,-1)

C=(5,-1)-->(-1,-5)

D=(7,1)-->(1,-7)

Now that we have the coordinates for A'B'C'D' we will graph both rectangles, (you can do this using Geogebra you wont need an account)once graphed we can draw a long straight line using a straightedge through points BA and B'A' to see that they eventually intersect and the line through B'A' goes through 1 on the x-axis.

The correct answer is:   [d]:   " 3x³ + 1x² + 6x  – 9 " .

explanation:

                ab – c² = ? ?

given:

a = x² ;

b = 3x + 2 ;

c = x – 3  ;

  c² = (x – 3)² = (x – 3)(x – 3) = x² – 3x – 3x + 9 = x² – 6x + 9 .

so:   ab – c² = (x²)(3x + 2) – (x² – 6x + 9) ;

                                          = 3x³  +  2x²  –  1(x² – 6x + 9)  ;  

                                          = 3x³ + 2x²  – 1x² +  6x – 9 ;

                            combine the "like terms" :

                                                  + 2x² – 1x² = 1x²  ;

    and rewrite:   " 3x³ + 1x² + 6x  – 9 "  ;     which is:   answer choice:   [d] .