Question

(5,-2),(6,4)(7,-2) are the vertices of isosceles triangle

Answer 1

The vertices of A(5, - 2), B(6, 4) and C(7, - 2)  are "an isosceles angled  triange".

Step-by-step explanation:

Let  A(5, - 2), B(6, 4) and C(7, - 2) are the vertices of a triangle.

$AB^{2} = (6 - 5)^{2}$ + (4 + 2)^{2}[/tex]  

= ( 1)^{2}[/tex] + (6 )^{2}[/tex]  

= 1 + 36 = 37

$BC^{2} = (7 - 6)^{2}$ + (- 2 - 4)^{2}[/tex]  

= (1 )^{2}[/tex] + (- 6 )^{2}[/tex]  

= 1 + 36 = 37

$CA^{2} = (7 - 5)^{2}$ + ( - 2 + 2)^{2}[/tex]  

= (2)^{2}[/tex] + (0)^{2}[/tex]  

= 4 + 0 = 4

∴ [tex]AB^{2} = [tex]BC^{2}

⇒ 37 = 37, the two sides of triangle are equal, it is proved.

The vertices of A(5, - 2), B(6, 4) and C(7, - 2)  are "an isosceles angled  triange".