Prove that the following four points will form a rectangle when connected in order by showing the diagonals are congruent. Show all work.
A(0, -3), B(-4, 0), C(2,8), D(6.5)

Step-by-step explanation:

If the diagonals of the rectangle are congruent,

AC = BD

By using formula to calculate the distance between two points,

Distance between two points =

Distance between A(0, -3) and C(2, 8),

AC =

     =

     =

Similarly, distance between two points B(-4, 0) and D(6, 5),

BD =

     =

     =

Therefore, both the diagonals are congruent.

Hence, given quadrilateral ABCD is a rectangle.

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

answer: a clock

step-by-step explanation: