Question

Which diagram shows the most useful positioning and accurate labeling of a kite in the coordinate plane?

Answer 1

Based on the given diagrams above, the correct answer would be the first diagram. The diagram that shows the most useful positioning and accurate labeling of a kite in the coordinate plane would be the first diagram. Hope this is the answer that you are looking for. 

Answer 2

Answer:  Second diagram and fourth diagram.

Step-by-step explanation:

A kite is a quadrilateral which has two pairs of congruent adjacent sides.

In diagram 1:

By the distance formula,

The sides of the given quadrilateral are $\sqrt{a^2+c^2}$,  $\sqrt{b^2+c^2}$, $\sqrt{b^2+d^2}$ and $\sqrt{a^2+d^2}$

Since, here a, b, c and d are unknown numbers,

Thus, this quadrilateral does not have any pair of congruent adjacent sides.

⇒ It is not a kite.

In diagram 2:

By the distance formula,

The sides of the given quadrilateral are $a$,  $a\sqrt{5}$, $a\sqrt{5}$ and $a$

Since, this quadrilateral has two pairs of congruent adjacent sides.

⇒ It is a kite.

In diagram 3:

By the distance formula,

The sides of the given quadrilateral are $a$,  $\sqrt{b^2+(c-a)^2}$, $\sqrt{(b-a)^2+c^2}$ and $a$

Since, here a, b, c and d are unknown numbers,

Thus, this quadrilateral only have only one pair of congruent adjacent sides.

⇒ It is not a kite.

In diagram 4:

By the distance formula,

The sides of the given quadrilateral are $\sqrt{b^2+c^2}$,  $\sqrt{b^2+c^2}$, $\sqrt{a^2+c^2}$ and $\sqrt{a^2+c^2}$

Since, this quadrilateral has two pairs of congruent adjacent sides.

⇒ It is a kite.