SOLUTION: I have been given the coordinates of a parallelogram. They are (2,1.5), (8,6) (16,6) and (10, 1.5). I have to find the perimeter. I know the answer is 31, but I just can't figur

Question 102398: I have been given the coordinates of a parallelogram. They are (2,1.5), (8,6) (16,6) and (10, 1.5). I have to find the perimeter. I know the answer is 31, but I just can't figure out how to find out the length of the diagonals. Please help.
Found 2 solutions by edjones, oberobic:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
the horizontals are 8 units long (graph paper).
coordinates of one of the slants is (2,1.5)(8,6)

Solved by pluggable solver: Distance between two points in two dimensions

The distance (denoted by d) between two points in two dimensions is given by the following formula:

Thus in our case, the required distance is

For more on this concept, refer to Distance formula.

So P=8*2+7.5*2=31
Ed

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The distance between each pair of points can be computed using the Pythagorean formula. Imagine that the line between any two points is the diagonal of a right triangle.
Consider the (x, y) pairs: (2, 1.5) and (8, 6). One side of the triangle is defined by a line that runs parallel to the x-axis, starting at 2 and ending at 8. The other side of the right triangle is a line parallel to the y-axis that runs from 1.5 to 6. The length of the side parallel to the x-axis is simply the difference in the x values = 8 - 2 = 6. The length of the side parallel to the y-axis (and therefore at right angles to the line parallel to the x-axis, by definition) is likewise the difference: 6 - 1.5 = 4.5.
So one side is 6 and the other 4.5. That means the diagonal line's length is the square root of ( 6^2 + 4.5^2 ).
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