Question

chack the weather (2,3) (3,4) (4,5) are vertices of isosceles triangle​​

Answer 1

Solution :-

Let A ( 2 , 3 ), B ( 3 , 4 ) and C ( 4 , 5 ) be the vertices.

$\bf Distance \ formula = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\bullet \sf \ A B = \sqrt{(3-2)^2+(4-3)^2}$

        $= \sf \sqrt{1^2+1^2} \\\\= \sqrt{1+1} \\\\= \sqrt{2} \ units$

$\bullet \sf \ BC = \sqrt{(4-3)^2+(5-4)^2}$

        $= \sf \sqrt{1^2+1^2} \\\\= \sqrt{1+1} \\\\= \sqrt{2} \ units$

$\bullet \sf \ AC = \sqrt{(4-2)^2+(5-3)^2}$

        $=\sf \sqrt{2^2+2^2} \\\\= \sqrt{4+4} \\\\= \sqrt{8} \ units$

AB = BC

That is,

Two sides are equal.

In an isosceles triangle two sides are equal.

So,

The given points are the vertices of an isosceles triangle.