Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.
Given: The 3 points are A(7, 10), B(-2, 5) and C(3, -4)
AB 
= √106 units …..(1)
BC 
= √106 units …..(2)
AC 
= √212 units
From equations 1 and 2, we have
⇒ AB = BC
Therefore, Δ ABC is an isosceles triangle …..(3)
Also, AB2 = 106 units …..(4)
BC2 = 106 units …..(5)
AC2 = 212 units …..(6)
From equations 4, 5 and 6, we have
AB2 + BC2 = AC2
So, it satisfies the Pythagoras theorem.
Δ ABC is right angled triangle …..(7)
From 3 and 7, we have
Δ ABC is an isosceles right angled triangle.
Hence, proved.
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