Show that the points A(– 5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles right – angled triangle. Calculate its area.
AB = √{(0 – 6)2 + (3 – (– 5))2}
= √{(– 6)2 + (8)2}
= √{36 + 64}
= √{100} = 10 units
BC = √{(9 – 3)2 + (8 – 0)2}
= √{(6)2 + (8)2}
= √{36 + 64}
= √{100} = 10 units
AC = √{(9 – (– 5))2 + (8 – 6)2}
= √{(14)2 + (2)2}
= √{196 + 4}
= √{200}
For the right angled triangle
AC2 = AB2 + BC2
AC2 = 200
AB2 + AC2 = 100 + 100 = 200
Since AB = BC
∴ ABC is an isosceles triangle.
Area = 1/2 (AB) (BC)
= 1/2 (10) (10)
= 1/2 (100)
= 50 sq units
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