Question

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

Answer 1

Answer: Second diagram and fourth diagram.

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
`√(a^2+c^2)`,
`√(b^2+c^2)`,
`√(b^2+d^2)` and
`√(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√(5)`,
`a√(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`,
`√(b^2+(c-a)^2)`,
`√((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
`√(b^2+c^2)`,
`√(b^2+c^2)`,
`√(a^2+c^2)` and
`√(a^2+c^2)`

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

⇒ It is a kite.

Answer 2

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.