Is this shape a kite, parallelogram, or a rhombus? The shape has coordinates: L(7,5) M(5,0) N(3,5) P(5,10).
4 Answers
a rhombus
Explanation:
The given coordinates:
L(7,5)
M(5,0)
N(3,5)
P(5,10).
The coordinates of the mid point of diagonal LN is
The coordinates of the mid point of diagonal MP is
So the coordinates of mid points of two diagonal being same they bisect each other, It is possible if the quadrilateral is a parallelogram.
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Now Checking the length of 4 sides
Length of LM =
Length of MN =
Length of NP =
Length of PL=
So the given quadrilateral is equilateral one and it would be a
rhombus
The second part is sufficient to prove everything required here.
Because equality in length of all sides also proves it a parallelogram as well as a special kite having all sides equal.
LMNP is a rhombus.
Explanation:
The points are
Distance between
LM is
MN is
NP is
LP is
As all the sides are equal, it is a rhombus.
Note If opposite (or alternate) sides are equal it is a parallelogram and if adjacent sides are equal, it is a kite.
The diagonals bisect at 90° so the shape is a rhombus.
Explanation:
As proved by the contributor, dk_ch, the shape is not a kite, but is at least a parallelogram, because the diagonals have the same midpoint and therefore bisect each other.
Finding the lengths of all the sides is a rather tedious process.
Another property of a rhombus is that the diagonals bisect at 90°.
Finding the gradient of each diagonal is a quick method of proving whether or not they are perpendicular to each other.
From the coordinates of the four vertices, it can be seen that
PM is a vertical line
NL is a horizontal line
The diagonals are therefore perpendicular and bisect each other.
It's not a kite or a square or a parallelogram. It's a rhombus .
Explanation:
To verify whether it's a kite.
For a kite, diagonals intersect each other at right angles but only one diagonal is bisected as against both in the case of rhombus and square.
Hence both diagonals are intersecting at right angles.
Since mid points of both the diagonals are the same, diagonals bisect each other at right angles and hence it's a rhombus or a square and not a kite.
Since
hence it's only a Rhombus.