Question

Show that the following points taken in order form an isosceles triangle

A ( 5,4) , B (2,0), C (-2,3 )​

Answer 1

Given:-

• Three coordinates , which are A(5,4) ; B(2,0) & C ( -2,3) .

To Prove :-

• The following coordinates are of an isosceles triangle.

Proof:-

We know that in a isosceles triangle two sides are equal .If we prove measure of any two sides equal and other side different then ,it will be a isosceles triangle.

Given coordinates are,

• A ( 5,4 )
• B (2,0)
• C (-2,3)

Using , Distance Formula ,

$\large{\boxed{\boxed{\red{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}}}$

Distance b/w A & B :-

⇒ D = √ [ (x2 - x1 )²+ (y2 - y1)² ]

⇒ D = √ [ ( 5-2)² + (4-0)² ]

⇒ D = √ 3² + 4²

⇒ D = √ 9 + 16

⇒ D = √25.

⇒ D = 5 .

____________________________________

Distance b/w B & C :-

⇒ D' = √ [ (x2 - x1)² + (y2 - y1 )² ]

⇒ D' = √ [ ( 2 + 2)² + (3-0)² ]

⇒ D' = √ [ 4² + 3² ]

⇒ D' = √ 16 + 9

⇒ D' = 25.

⇒ D = 5 .

Hence we found two sides of the triangle equal . So, we can conclude that the ∆ is a isosceles triangle .

$\Large{\boxed{\pink{\sf Hence \:\:Proved ! }}}$