Three friends live in houses with backyards adjacent to a neighborhood bike path. They decide to have a round-robin party using their three homes, inviting their friends to start at one house and then move to each of the other two. If one friend's house is centered at the origin, then the location of the other homes are (5,12) and (13,0) . Write a coordinate proof to prove that the triangle formed by these three homes is isosceles.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The given vertices are making a triangle as shown below in the figure.

Distance between A(5,12) and O(0,0) is

⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]

⇒ 13

Distance between B(13,0) and O(0,0) is

⇒ [tex]\sqrt{(13 - 0)^2}[/tex]

⇒ 13

Since the two sides are the same so triangle will be isosceles.

Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".

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