SOLUTION: show that midpoint of the side of the rectangle are the vertices of rhombus and its vertices are (0,0),(a,0),(0,b),and (a,b)
Algebra.Com
Question 452127: show that midpoint of the side of the rectangle are the vertices of rhombus and its vertices are (0,0),(a,0),(0,b),and (a,b)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume what you are trying to do is to prove that the quadrilateral formed by joining all of the adjacent side midpoints of the side of a general rectangle is a rhombus and that the vertices of the original rectangle are the four you specified.
Given my presumption, the four midpoints are
)
)
)
and
)
To prove a rhombus it is sufficient to prove that all four sides have the same measure. (This is sufficiently general because a square is a special case of a rhombus).
Use the distance formula to determine the length of one of the sides of the quadrilateral. Let's begin with the segment defined by the first two endpoints above:
^2\ +\ \left(\frac{b}{2}\ -\ b\right)^2}\ =\ \frac{\sqrt{a^2\ +\ b^2}}{2})
Now all you have to do is to show that the distances from the 2nd to the 3rd, 3rd to the 4th, and 4th to the 1st points are all the same as that which we just calculated.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
: Show that the points, A(0, 0), B(0, 4), and C(4, 0) are the vertices of a right... (answered by greenestamps)
prove that the diagonals of rectangle are equal in length,whoes vertices... (answered by solver91311)
Show that A(1,1),B(4,1),C(3,-2) and D(0,-2) are the vertices of a... (answered by Alan3354,greenestamps)
Given that the four points A(1,2), B(2,-5), C(7,0) and D(p,q) are the vertices of rhombus (answered by mananth)
SHOW in two ways that (0,-5) (3,-4) (8,0) and (5,-1) are the vertices of a rhombus.... (answered by stanbon,rothauserc)
Show that the points (1,-3),(4,3),(3,7) and (0,-1) are vertices of a... (answered by Alan3354)
If. A(-8;6),B,C and D(3;9) are vertices of a rhombus. The equation for AC is 3y=-x+10... (answered by richwmiller,Edwin McCravy)
a) Show that the triangle with vertices D(-1,0), E(1,0) and F(0,√3) is equilateral. (answered by robertb)
show that the points (1,1) (0,-3) and (9,6) are the vertices of the square and find its... (answered by robertb)
