Question

Show that the points A(3, 0), B(6, 4) and C(-1, 3) are the vertices of an isosceles right triangle.

Answer 1

Let A (3,0) B (6,4) and C (-1,3)
now use distance formula ,
AB=$\sqrt{(}6-3{)}^2+(4-0{)}^2$=$\sqrt{(}25)$=5
BC=$\sqrt{(}-1-6{)}^2+(3-4{)}^2$=$\sqrt{(}50)$
CA =$\sqrt{(}3+1{)}^2+(-3{)}^2$=5.

you see ,
$B{C}^2$ =$A{C}^2$+ $A{B}^2$
which is related to Pythagoras theorem .
hence , ABC is the vertices of right angle isoceles triangle .in which A is right angle .

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