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The given quadrilateral is a kite.
Given: Point A (2, 4), B (-2, -5), C (7, -1) and D (7, 4)
Firstly, we find the distance between AD and DC
AD =
⇒ AD =
⇒ AD = 5
DC =
⇒ DC =
⇒ DC = 5
Hence, AD = DC = 5
Now, find the distance between AB and BC
AB =
⇒ AB =
⇒ AB =
⇒ AB =
BC =
⇒ BC =
⇒ BC =
⇒ BC =
Hence, AB = BC = √97
In the given quadrilateral, the two pair is of equal length and these sides are adjacent to each other.
Hence, it follows the property of kite.
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