Show that the points A(7, 10), B(– 2, 5) and C(3, – 4) are the vertices of an isosceles right triangle.
In an isosceles triangle any two sides are equal.
AB = √{(– 2 – 7)2 + (5 – 10)2}
= √{(– 9)2 + (– 5)2}
= √{81 + 25}
= √{106}
BC = √{(– 4 – 5)2 + (3 – (– 2))2}
= √{(– 9)2 + (5)2}
= √{81 + 25}
= √{106}
AB = BC
∴ It is an isosceles triangle.
19