Question

A(-4, -7), B(-1, 2), C(8,5) and D(5, 4) are the
vertices of rhombus ABCD​

Answer 1

hope so it is useful for you

Answer 2

Correct Question :-

Find out whether the vertices A(-4, -7) , B(-1,2) , C(8,5) and D(5,4) are vertices of a rhombus.

Solution :-

We have the vertices of a figure, that may form a rhombus. With the vertices we can find the distance between each consecutive vertex.

As we know, All the four sides of rhombus are equal that is a first step towards proving whether the given vertices form a rhombus or not.

So, Let's find the distance b/w each consecutive vertex to find if they are same.

Using distance formula, which is given by,

• d = √{ (x₂ - x₁)² + (y₂ - y₁)² }

Now, Let's find the distance

⇒ AB = √{ (-1 - (-4))² + (2 - (-7)² }

⇒ AB = √{ (3)² + (9)² }

⇒ AB = √90

And,

⇒ BC = √{ (8 - (-1))² + (5 - 2)² }

⇒ BC = √{ (9)² + (3)² }

⇒ BC = √90

Further,

⇒ CD = √{ (5 - 8)² + (4 - 5)² }

⇒ CD = √{ (-3)² + (-1)² }

⇒ CD = √10

Similarly,

⇒ CA = √{ (5 - (-4))² + (4 - (-7))² }

⇒ CA = √{ (9)² + (11)² }

⇒ CA = √202

Because, AB = BC ≠ CD ≠ CA hence the given vertices doesn't form a Rhombus as all four sides of a rhombus are equal.