The coordinates for a rhombus are given as (2a,,,0) and (0,-2b) write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry be sure to include the formulas

Step-by-step explanation:

Let the points of rhombus be A(2a,0), B(0,2b), C(-2a,0) and D(0,-2b).

Let midpoints of  AB be P, then

Let the mid point of BC be Q, then

Let the mid point of CD be R, then

and Let the mid point of DA be S, then

It can be seen that P lies in quadrant I, Q in Quadrant II, R in III and S in IV, Further P and Q are the reflections of each other in y-axis, Q and R are the reflections of each other in x-axis,R  and  S  are reflection of each other in  y -axis and  S  and  P are reflection of each other in  x -axis.

Hence, the mid points of the rhombus  forms the rectangle.

me

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.