Parallelogram ABCD has vertices at A(–1, 1), B(7, 3), C(5, –1), and D(–3, –3). What is the perimeter?
The answers have square roots in them and I'm trying to figure out why...as I had thought I would plot and add up the sides?
thanks for any help that can be offered...
More Questions From This User See All
Answers & Comments
Verified answer
The diagonals are BD and AC
The way that you know that is to compute all six of the lengths and those pairs that are of equal lengths are the sides of the parallelogram. Since I am from the pre-calculator era I do that in my head, with the following results:
__ . ___
AD = BC..........and
__ . ___
AB = CD
However I have made a graph of this problem for you. To see it click on the following link:
http://i369.photobucket.com/albums/oo133/gerryrain...
Plotting the four points on a sheet of graph paper is probably the easiest way to tell the difference between the sides and the diagonals.
The distance between A and D is:
sqrt(2^2 + 4^2) = sqrt(20) = sqrt(4*5) = 2*sqrt(5)
The distance between A and B is:
sqrt(8^2 + 2^2) = sqrt(68) = sqrt(4*17) = 2*sqrt(17)
So you have two sides of length 2 * sqrt(5) for a total length of 4 * sqrt(5) and you have two sides of length 2*sqrt(17) for a total length of 4 * sqrt(17)
The perimeter is: 4 * [sqrt(5) + sqrt(17)]....<<<<....Answer
.