Show that the points A(3, 0), B(6, 4) and C(– 1, 3) are the vertices of an isosceles right triangle.
In an isosceles triangle any two sides are equal.
AB = √{(6 – 3)2 + (4 – 0)2}
= √{(3)2 + (4)2}
= √{9 + 16}
= √{25} = 5 units
BC = √{(– 1 – 6)2 + (3 – 4)2}
= √{(– 7)2 + (– 1)2}
= √{49 + 1}
= √{50}
AC = √{(– 1 – 3)2 + (3 – 0)2}
= √{(– 4)2 + (3)2}
= √{16 + 9}
= √{25} = 5 units
AB = AC
∴ It is an isosceles triangle.
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