SOLUTION: quadrilateral with midpoints joined Quadrilateral ABCD has vertices A(-2,6), B (4,5), C(3,-2), D(-5,1). Points E, F, G, and H are midpoints of the sides of the quadrilateral as sh

Algebra ->  Parallelograms -> SOLUTION: quadrilateral with midpoints joined Quadrilateral ABCD has vertices A(-2,6), B (4,5), C(3,-2), D(-5,1). Points E, F, G, and H are midpoints of the sides of the quadrilateral as sh      Log On


   

Question 1067049: quadrilateral with midpoints joined
Quadrilateral ABCD has vertices A(-2,6), B (4,5), C(3,-2), D(-5,1). Points E, F, G, and H are midpoints of the sides of the quadrilateral as shown in the graph. Find the perimeter of quadrilateral EFGH. Round your answer to the nearest tenth.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw the diagonals,
you realize that each diagonal
divides the quadrilatetal into two triangles,
and the segments connecting the midpoints
of the sides of ABCD
are the midsegments of those triangles.
As such, they are parallel to one or another diagonal,
and half as long as that diagonal.
So, the new quadrilateral is a parallelogram,
and it's perimeter is the sum of the lengths
of the diagonal of ABCD.

The lengths of the diagonals are
and
,
so the perimeter of EFGH is
highlight%28sqrt%2889%29%2Bsqrt%2897%29%29