Question

Prove that the points (3,0),(6,4),(-1,3) are the vertices of a right angled isosceles triangle

Answer 1

Answer:

For easy reference, call the points A=(3,0), B=(6,4) and C=(-1,3).

• AB²  =  (6-3)² + (4-0)²  =  3² + 4²  =  9 + 16  =  25
• BC²  =  (6+1)² + (4-3)²  =  7² + 1²  =  49 + 1  =  50
• CA²  =  (3+1)² + (0-3)²  =  4² + 3²  = 16 + 9 = 25

Since AB² = CA² (and so AB=CA), the triangle is isosceles.

Since AB² + CA² = BC², the triangle is right angled at A (by the converse of Pythagoras' Theorem).