Question

Prove that P(2,3), (3, 4), R(5, 6) and S(4,5) are thevertices of a rhombus​

Answer 1

Solution :-

Given coordinates to us are ,

• P(2,3) .
• Q(3,4).
• R(5,6)
• S(4,5)

Here it is asked to Prove that these are vertices of Rhombus . So we know that all sides of a Rhombus are equal .So if we show that value of all sides lenght are equal , then it will be a Rhombus .

We will use Distance Formula .

Now , here ,

Distance between P and Q :

⇒ x = √ (2 - 3)² + (3-4)² .

⇒ x = √ (-1)² + (-1)² .

⇒ x = √ 1 + 1 .

⇒ x = √2 .

Distance between Q and S :

⇒ x =√ [ (3-4)² + (5-4)².

⇒x = √ 1² + 1² .

⇒ x = √ 1 + 1 .

⇒ x = √2 .

Similarly we can prove other distances equal.